Make the indicated trigonometric substitution in the given algebraic expression and simplify (see Example 7). Assume that 0 < 0< T/2. V1+x?, x = tan(O)

Q: Prove the following Sin hZ=0

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Q: If we make the substitution a =4 tan 0 (for –<0<), then sin 0 is equal to which of the following…

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Q: Given that tan² O +1 00|m O ± IN 11 8 000 = 100 8S 3 8, what is the value of sec e?

A: I have stated the used formula in the solution.

Q: Given that sin t = 1/2 and 0 ≤ t &lt; π/ 2, find the value of cos t using a trigonometric identity.

A: Given

Q: 2. Use the fundamental identity to write two functions for cos a in terms of sin a. Indicate which…

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Q: Simplify the lefthandside so that LHS RHS: 2 1 tan(a) + 1+ sin(a) 1- sin(a) cos(a) 1+ sin(a) 1-…

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Q: Make the indicated trigonometric substitution in the given algebraic expression and simplify…

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Q: 1. Explain the steps in verifying that the following equation is an identity. cos x sec x + tan x =…

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Q: Prove the formula eix cos(x) + i sin(x) %3D Use this to evaluate e2i

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Q: 11. Evaluate the exact value of each of the following trig e> a) tan-(-V3) b) sec (sin" (-))

A: Answer and explanation is given below

Q: 6. Explain the steps in verifying that the following equation is an identity. sec x sin x = cot x…

A: We have given equation  Taking left side of equation  LHS = secxsinx-sinxcosx           =…

Q: 4. Explain the steps in verifying that the following equation is an identity. sec sin a sin r cos a…

A: Given equation: secxsinx-sinxcosx=cotx

Q: sin x xp = + cos x 1+c

A: ∫0π2sin x1+cos xdx Formula ∫xndx=xn+1n+1+C

Q: 3. Which is equal to (sin a + cos a) +(sin r cos a) using identities? CO O 2 -2 О-1

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Q: Evaluate the following : e#/2 (a) sin(In 0) dê.

A: SOLUTION-

Q: Evaluate the expression under the given conditions. V5 o in Quadrant I sin(0 + o); sin(0) = , O in…

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Q: Find the exact value of the expression whenever it is defined.

A: (a) sin-1-22 -π2≤x≤π2 sin x=-22 multiply and divide by 12 sin x =12  sin x = π4 sin-1-22=π4

Q: If we have the function f(x) = sin x and f(a) =,what is f(a) + f(a+2r)+f(a+41). Solve it by using…

A: The given function is: f(x)=sin(x)f(a)=13

Q: -517 da. Verify that the equation (secx + tan x) cos x - 1 = sin x is true for: (sec +tan)cos- =sin?…

A: Given,       (sec x + tan x) cos x - 1= sin x

Q: In a brief, substansive, grammatically correct statement, describe the first step you are inclined…

A: In a brief, substansive, grammatically correct statement, describe the first step you are inclined…

Q: Use the given substitution to express the given radical expression as a trigonometric function…

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Q: ind the exact value(s) of sin (8), if cos(8) , and 0se<a xpress v3 sin(x) + v2 cos(x) in the form…

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Q: sin 3t? limt-o 1-cos 2t

A: To evaluate: limt→0sin 3t21-cos 2t 00 form

Q: b. 3 tan e sin e-2 tan e 0

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Q: 12. Explain why using trigonometric substitution with x = a tan u often involves a triangle with…

A: Consider the right triangle below with angle u , opposite side x and adjacent side a.

Q: For all values of α for which the expression is defined, tan(2α)/cos^2(α)= ?

A: let  f(α)=tan2αcos2α

Q: Simplify the lefthandside so that LHS = RHS: 1+ cos(a) cos(a) 1 tan(a) sin(a) 1 1+ cos(a) 1- cos(a)

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Q: Write the given expression as an algebraic expression. sin(arcsin x + arccos x) 2 1- x* + X 2 + 1 1-…

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Q: expand the formula for sin(A+B)

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Q: Given that sin t = 3/5 and 0 ≤ t &lt; π/ 2, find the value of cos t using a trigonometric identity.

A: We have to find cos t using trigonometric identity where, sin t=35 and 0≤t&lt;π2 We know the…

Q: tan? x 1-cos x sec? x + sec x Prove

A: We can solve it by multiplying (1+cosx) in numerator and denominator.

Q: Show that the following general equation x = c1 cos(/t) + c2 sin(\/t) k m can be transformed into: C…

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Q: Evaluate the following using the TRIGONOMETRIC SUBSTITUTION METHOD: 1.5 dx

A: Given: I=∫dxx2x2+4 For evaluating given integral, we substitute x=2tanθ…

Q: If sin A =2/3 with A in the interval 0° &lt;= A &lt;= 90°, find       tan A/2

A: Given: sin A = 23   with  0° ≤ A ≤ 90° To find: The value of  tan A2.

Q: Simplify (Tn +n) into an expression without fractions and (1+sin A 1-si involving only a single…

A: We will simplify the expression as following.

Q: T Sin ³ de 3 1-cose

A: I have stated the used formulas in the solution

Q: Suppose 0 <m(8)<, and x=2 sec(0). What is the resulting expression if we write √x² - 4 as a…

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Q: Using a suitable substitution, (sin x cos“ x) dx can be 4 (A) - f u*du (B)

A: Given: ∫0π2sinxcos4xdx

Q: Find the exact value of the following expression. V3 1 sin | 2

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Q: to make it invertable? Which trigonometric function requires a domain restriction of 2 2 O A. f(x)=…

A: To find: the trigonometric function which requires a domain restriction of -π2,π2 to make it…

Q: Solve for tan(A – B) if sin(A) = and A is in Q1 and if cos(B) = - and B is in Q3. 25 [Hint: Use the…

A: Given: sin(A) = 4/5 and A is in Q1 and cos(B) = −7/25 and B is  in Q3.

Q: 51. Compute x² _ and then using the identity dx in two ways and verify that the answers agree: first…

A: Assume the given integral be I. I can be integrated via trigonometric substitution by substituting…

Q: (9) Verify the following (a) cos e + sin 0 tan e = sec e %3D

A: As per guidelines we can answer only one question at a time, so if you need more answer kindly…

Q: Evaluate the expression under the given conditions. 3 sin(0/2); tan(0): O in Quadrant IV (assume 0 <…

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Q: 15. Explain the steps in verifying that the following equation is an identity. sec a sin e sin a cot…

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Q: If sin A =2/3 with A in the interval 0° &lt;= A &lt;= 90°, find       sin A/2

A: sinA=23,   0≤A≤90° By using the identity sin2A+cos2A=1, we get…

Q: By an appropriate trigonometric substitution, Choices: √ √10 sin sin 0 cos de cos √10 sin 0 1 /10…

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Q: 4. Write an equivalent expression for sin*(x) that does not contain powers of trigonometric…

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