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

Q: 3. Find the value of sin(2x) given that sin x = and x is in QII.

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Q: Given that the sin x = 2/5 and cos x = -1/4 with sin x in Q1 and cos x in Q3, find sin( sin x - cos…

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

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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: Find sin(2x), cos(2x), and tan(2x) from the given information. tan(x) = - 4 - cos(x) > 0 sin(2x) =…

A: Answer

Q: 3. Prove that the identity is true. sin*t- cost = tan²t-1 cos't

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

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Q: Verify the identity: (sin x - sin y)/(cos x - cos y) = -cot (x+y)/2

A: sinx-sinycosx-cosy=2cosx+y2sinx-y2-2sinx+y2sinx-y2=-cosx+y2sinx+y2=-cotx+y2…

Q: * Prove: sin x = cos COS 2- 2cos x

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Q: 3. If cos x = -, find sin(2x) given sin x < 0. -3 O O

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

A: Given,           tan(x) =-16, cos(x) &gt; 0

Q: sin x cos" п — 1 n 2 2, | co cos"-2 x d.x Show that for cos" x dx Use this to find cos4. x dx.

A: Given, ∫cos4xdx

Q: Let y=f(x)=sin^2(x)-cos(x)+2sin(x)+x find f'(x), factor f'(x) and determine the critcal values on…

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Q: If * = 2 tan(0), then a. cos(0) Vx2 + 2 Ob. cos(x) = Vx2 + 4 c. sin(8) = Vx2 +4 O d. cot(0) 2 е.…

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Q: The expression sin(x) cos(x) - cos³(x) simplifies to f(x) sin(x) Determine f(x).

A: The given expression is: sinxcosx-cos3x As we know the trigonometric identity; 1). cosx=1secx 2).…

Q: If z =7 tan 0, express sin (20) as a function of z. sin (20) =

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

A: Solution:-  This types of trignometric integrals can be solve by reduction formula of integral.

Q: Given that sin2   x + cos2  x = 1 and sin x = −√2/5, what is the possible value of cos x

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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: Which is equal to (sin⁡x+cos⁡x)^2+(sin⁡x−cos⁡x)^2 using identities?

A: Now we use identity  Sin2x +cos2x =1 And formula (a+b)2= a2 +b2 + 2ab  (a-b)2 = a2 + b2 - 2ab

Q: Assuming that |a| < 1, find the value of cosh ax dr. cosh x

A: It is given that,a&lt;1, we have to find the value of              ∫0∞coshaxcoshxdx

Q: Prove ONE of the follow sin x+ cos 2x-1 tan x %3D a) cos x-sin 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: Verify the identity. (Simplify at each step.) 6 cos (T/2) – x 6 tan x sin (1/2) – x 6 cos (u/2) – x…

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Q: the exprression csc x/sec x  is equivalent to: 1.  sin x 2. cos x 3. tan x 4. cot x

A: *to find:-  csc x/sec x = ?

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: Prove the below cos' x sin 3x + sin' x cos 3x 3 sin 4x 4 II

A: Simplification of trigonometry function

Q: Find x so that sin 3x + 10 cos x+ %3D

A: Here we have to find the value of x. The solution is following.

Q: Verify the identity. 1- sin 0 cos e cos 0 1- sin 0 =2 sec e To verify the identity, start with the…

A: We can verify the identity as below using trigonometric formulas.

Q: If ln sin x = 1 + ln cos x, then x is equal to what.

A: Given that , lnsinx=1+lncosx find value of x.

Q: 1+ cos x sin x 7. Verify: ¹ 11 csc x + cotx

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Q: Q4) Prove that 1- Cos +x) = sin x, 2- (sin x +cos x) sec x see' x

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Q: Prove the identity. ex(1- sin'x) = So cosx | %3D

A: Prove the identity- Secx(1 - sin2x) = cosx. We know that : sin2x + cos2x = 1 Here i attached…

Q: 278. Suppose that sin(ln x) = 3, and that sin(ln y) = }. If 0 < ln x < and 0 < ln y < , use the…

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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: If cos x= √7/4 and 3 π/2 (less than) x (less than) 2 π, find tan x/2

A: If cos x= √7/4 and 3π/2 &lt; x 2π, find tan x/2

Q: Let I = S sin 2xdx be given. After substituting y = tan x, how can 5 cos? x+7 sin? x the integral I…

A: Given :

Q: If csc(x) = 3, for 90° < x < 180°, then sin() V2 1 V6 2 COS 2 V3+2v2 V6 V 2 - 1 tan 2 V 3 + 2v2

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Q: from the given information. tan(x) = 2,   0° < x < 90° sin x/2= cos x/2= tan x/2=

A: Given tan(x) = 2 So first find x ,   where 0° &lt; x &lt; 90°

Q: Find x where 0 ≤ x ≤ 2π. cos x - tan²x = 1

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Q: sin(x - ) = -COS X 2

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

A: Given that: ∫sin24(x+2)dx

Q: If f (x) = - sin(x), then f (10) (x) is equal to = - sin(x), thenf (10) (x) is equal to A - sin(x) B…

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Q: . Prove only 1 of the 2 identities given. sin x 1-cosx = 2 csc x 1-cos x sinx -) 1- sin? x – sin² y…

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Q: 1. Which expression is equal to sec x tan z sin x using identities?

A: We can use simple trigonometric identities to solve the given equation.

Q: 52. Verify that f(x) sin x is an odd function and u fact to show that '3 sin x dx < 1 -2

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

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Q: Find a simpler for for cos (x – *) O sin x - sin x O cos x - cos x COS x

A: On solving ,we get