For Exercises 7–14, verify the identity. sinxtan?x – sinxr 7. cosxtanx + cosx tanx(tan.x – 1) 3 sin'x – sinx – 2 8. cosxsinx - cos.x 3 tanx + 2 secx 1 1 9. cscx - 1 1 - sinx 10. 2 tanxsecx cscx + 1 cosx 1 + sinx 11. In|cscx| + In|tan.x| = In|sec.x| cosx 12. In/tan.x| – In|sin.x| + In|cos.x| = 0 13. cosx + sin(-x)tan(-x) = secx 14. [csc(-x) + 1](cscx + 1) = -cot?x

Q: S./2(sec²x – cos²?x – tan²x)sin5xcosxdx -

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Q: (c) Prove that sin x 7C sin 2 x2 dx +4x+5

A: The integral function is ∫-∞∞sinxx2+4x+5dx

Q: tan3x)dx tan Evaluate: cos23x A - In|sec (tan3x)|+C - In|cos (tan3x)| +C B © In cos(tan3x)| +C in…

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Q: To begin evaluating S sin*(x) · cos³(x)dx, express a. sin*x to (sin²x)²and use the identity sin²x…

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Q: The suitable substitution to evaluate / sin²4(x +2) dx is (1- cos8(r + 2)] [1+cos8(x+2)] None 1 [1-…

A: We have to find the suitable substitution to evaluate the following integral -  ∫sin24(x+2) dx

Q: Q3) Use the addition formulas to derive the identity of (cos (x --): sin x ) %3D

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Q: Show that L-1{ = (sin hat sin at) s4+4a4, 2а2

A: To find Inverse Laplace transform of ss4+4a4: write ss4+4a4 as  ss2+2a22-2as2 Then the denominator…

Q: tan( tan3x)dx Evaluate: cos²3x A 3 -In sec(tan3x)| + C B -n|cos( tan3x)| + C In|cos (tan3x)| +C (D D…

A: the given integral,      ∫tan(tan 3x)dxcos23x

Q: EX-15- Prove that : a) Sec-'x= Cos- ! b) Sin-' (-x)=-Sin-'x

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Q: If cos(0) 1 and 0 satisfies T < 0 < , find sin(0). 2 - sin(0) = %3D

A: Given: cos θ=-16 &amp; π&lt; θ&lt;3π2 To determine: sin θ

Q: ... at verifies the identity. OC. B. sin 9x cos 7x - cos 9x sin 7x = sin (9x – 7x) = sin 2x sin 9x…

A: Given query is to find the correct option to prove the identity.

Q: 5. Find y', if y = 2cosx sin2x – sinx cos2x %3D

A: NOTE:according to company rules I need to solve first question when multiple questions are posted

Q: 5. Find y', if y 2cosx sin2x – sinx cos2x %3D

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Q: Show that x² + 1 cos{arctan[sin(arccot x)]} = V x² + 2

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Q: To evaluate sin*2x cos 2x dx , the identities to be used is/are: 1+ cos4x A sin4x & 2 2 B cos²2x= 1-…

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Q: Please find all 0 ≤ 0 ≤ 2π, for which ... (a) tan () = √3 (b) 3 sin²(0)+ 4 = 5 (c) 2 cos(ln(x² + e²)…

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Q: Q4: Prove that: cos?x – sin?x cos²x - 1- tan?x

A: We need to prove that cos2x-sin2xcos2x=1-tan2x We will use tanx =sin xcos x

Q: Find sin 2x, cos 2x, and tan 2x if tanx = - and x terminates in quadrant II. sin 2x cos 2x %3D tan…

A: Given data,  tan(x)= -(2/3) Where x in 2nd quadrant. A)sin(2x)=? We know that;…

Q: Find sin(2x), cos(2x), and tan(2x) from the given tan(x) = -, cos(x) > 0 %3D sin(2x) = %3D cos(2x) =…

A: Given: tanx=-16,   cosx&gt;0 sin2x can be calculated as, sin2x=2tanx1+tan2x          =2×-161+-162…

Q: 1. Differentiate the following with respect to the variable given. 1 cosx 2 sin x tan 2. Given the…

A: We can solve the given problem as follows:

Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin301² [cos 40+ i sin40 1³[cos 20-i sin2015 using De…

A: The given expression,      cos 2θ-isin 2θ8cos 3θ+isin 3θ2cos 4θ+isin 4θ3cos 2θ-isin 2θ5 De Moivre's…

Q: Find sin 2x, cos 2x, and tan2.x if sinx= -- 3 and x terminates in quadrant IV. V13 sin 2x cos 2x tan…

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Q: d. Show that sin 8x + sin 4x cos8x-cos4x = -cot(2x)

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Q: (i) Prove that sec 3x(sin 3x-2sin' 3x)= tan 3xcos 6x. (ii) Hence find, for 0s.xs, the values of x in…

A: Trigonometric equation

Q: ( tan( tan3x)dx Evaluate: cos²3x A -In |sec(tan3x)| + C 3 |cos(tan3x)|+C B © --n |sin(tan3x)|+c O…

A: Evaluate: I=∫tantan 3xcos2 3xdx

Q: Prove (Start either from the LHS or the RHS but DO NOT work from both sides at the same time) 1.…

A: sin2x=1-cos2x and,  tanx= sin(x)/cos(x)

Q: evaluate y' for y = cos12x - sin^2 6x

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Q: ind sin2x, cos 2x, and tan 2.x if tanx = -2 and x terminates in guadrant II. %3D sin 2x ? cos 2x tan…

A: In second quadrant sin is positive and cos &amp; tan are negative.

Q: 1 what are possible values of cos x and tanx? 2 If sinx= Select one: V3 and tanx= 2 1 a. cosx= V3 V3…

A: Consider the right triangle with one angle x degree. Let a be the length of the adjacent side and b…

Q: Evaluate: tan( 4x- -In |cos (4x + 3)|+C B -In |sin(4x + 3)|+C -In |cse (4x + 3)|+C -In \sec (4x +…

A: the given integral,        ∫tan(4x+3) dx

Q: Choose the correct answer If f(x)=ln⁡(cos⁡(3x)) , then f"(x) =…  -9 sec2 (3x)  9 cos2 (3x)  9 tan2…

A: Derivative problem....

Q: 05 of the ac 42. Use the identity sin 2x = 2 sin x cos x to find the derivative of sin 2.x. Then use…

A: Find the derivative sin2x

Q: TO For x such that 0 < x<, the expression 2. V1-cosx V1- sin'x COS"X is equivalent to: sin x COS X

A: I am solving this in step 2

Q: х Given that t= tan , show that: 1-1? 2t d) sin x = 1+t? e) cosx = 1+1? 2t f) tanx = 1-?

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Q: y = cos (tan (3x)) A. -9cos? (tan (3x))sin (tan (3x)) sec (x) B. -9cos? (tan (3x))sin (tan (x))…

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Q: Prove that 3x Question 4 (i) sin(tan-(3x)) cos(tan-(3x)) = 1+ 9x² d 1 (ii)- sin-'(/) = dx 2a/1 – x

A: A detailed solution is given below.

Q: Evaluate: | tan(4x + 3)dx i -In |cos (4x+3)|+C A COS 4 В 4 - In |sin (4x + 3)|+C In |csc (4x+3)|+C D…

A: Given: ∫tan(4x+3)dx =∫sin(4x+3)cos(4x+3)dx Substitute :…

Q: The suitable substitution to evaluate | sin² 4(x + 2) dx is None O A. - cos8(r +2)] [1- cos4(r+ 2)]…

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Q: Differentiate the following 1. g(x) = x³ cos x 2. g(x) = 4 sec x + tan x sinx 3. g(x) =- 1+cosx tanx…

A: 1) g(x) = x3cosx2) g(x) = 4secx+tanx3) g(x) = sinx1+cosx4) g(x) = tanx secx5) g(x) = x1+sinx

Q: / tan( 4x + 3) dx Evaluate: (A) –In |cos (4x+ 3)|+C 4 B 4 ® -im [sin(4r + 3)| +C В –In |csc…

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Q: Show that n/2 sin x dx sin x + coS X %3D 4

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Q: tan( tan3x) dx Evaluate: cos²3x A - In|sec ( tan3x)|+C 3 B -In|cos( tan3x)|+C В 3 © In|cos(…

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Q: Show that : |sin x |= CoS nX Σ n2 even 414 2/7

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Q: Find sin 2x, cos 2x, and tan 2x if sinx= and x terminates in guadrant IV. sin 2x %3D cos 2x %3D tan…

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Q: Use the Substitution Rule to prove that∫sin2ax dx =(x/2) -(sin(2ax)/4a )+ C

A: Given:∫ sin2 ax dx

Q: Evaluate: tan(4x +3)dx A 4 A -In |cos (4x + 3)|+c B -In |sin(4x + 3)|+C 1 (c) -In |csc (4x+3)|+C D…

A: Integral calculus is the fundamental discovery was the link that exists between this and the…

Q: Show that 1 − cos x = x2/2 with an error less than 0.003 for |x| &lt; 1/2.

A: Given: 1-cos x =x22;    |error|&lt;0.003Formula:  The…

Q: Verify the identity. sin 3x 1 = 2 cos x- %3D sec x 2 - sin 2x

A: Given: Verify the identity sin3xsin2x=2cosx-12secx for verifying given identity we solve left hand…

Q: In sine sin -1x os (sin-!x) + C cos V1-x? 1-x² A) True В False

A: To check:  ∫sin(elnsin-1x)dx1-x2=-cos(sin-1x)+C is true or false.