Prove the following are identities using the definitions of the inverse trig functions and show all steps. Assume the relevant part of the cofunction theorem for part b, that is cot(theta)=tan(pi/2 - theta) for all angles theta with theta cannot equal npi for each integer n. a: sec^-1x=cos^-1 1/x b:cot^-1x= pi/2- tan^-1 x

Q: ) Prove cot 2 = tan u using the addition/subtraction formulas.

A: Given : cotπ2-u= tanu

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Q: Verify the identity. sin (7x) – sin (3x) = - cot (5x) cos (7x) - cos (3x) ..... Start with the…

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Q: 15. Using the identities, find cotx and secx if sinx = 1/4 and cosx > 0. %3D

A: Question number 15,Given,          sinx=14 and cosx>0

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Q: Verify the identity. sin (3x) - sin (9x) cot (6x) cos (3x) - cos (9x) Start with the numerator of…

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Q: Verify that the equation is an identity. (Hint: sin 2x = sin (x+ x)) sin 2x = 2 sin x cos x…

A: Given identity issin 2x = 2 sinx cos x prove it?

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A: giventanx=-34   90°&lt;x&lt;180°  we know that…

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Q: Verify the identity. cos 3x + cos x = 4 cos3 x - 2 cos x Working with the left-hand side, use a…

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

A: Given, cossin-11517-sin-1817 now find value of the expression we know, sin-11517=cos-1817…

Q: 8-Prove the following identities. ( [Tan2x/ (secx -1)] -1= secx Cos x+[sin2x/(1+cosx)] = 1

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Q: Verify the identity: cot2 2x + cos2 2x + sin2 2x = csc2 2x

A: The given identity is ot2 2x + cos2 2x + sin2 2x = csc2 2x

Q: Prove the identity. sin(3x) + sin(9x)_ cos(3x) + cos(9x) Use the Sum-to-Product Formulas and then…

A: Using the sum to product formula we get: sin(3x)+sin(9x)cos(3x)+cos(9x)=2sin6xcos3x2cos(6x)cos(3x)

Q: Use the fundamental identities to fully simplify sin (-x) cos (-x) sec (-x).

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Q: Prove the following identities. Show all steps for full marks. a) COS Зл 2 + x = sin x AND, do only…

A: We need to prove the following: a) cos3π2+x = sinxc) tanx-sinxsin3x = secx1+cosx

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Q: Prove the identity. 1+ sinx cosx =2 seex cosx 1+ sinx

A: We need to prove the following identity 1+sinxcosx+cosx1+sinx = 2secx

Q: 6. Use the identities to find cscx and cotx if secx =7 and sinx < 0. Show all work.

A: Solve question number 6 as asked by the user .

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A: Given, We have to proof a. (1 + sin θ)(1 - sin θ) = 1/sec2 θ b. log tan θ = log sin θ - log cos θ

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A: Devide the whole left side by Cos17° and use formula of tan(a+b)

Q: On a separate sheet of paper, prove the following is an identity. cosX/1+sinX + 1+sinX/cosX = 2secX

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

Q: . Prove that cos(sin^-1x)=sqrt(1-x^2) for -1<=x<=1. 12. Simplify each expression as in exercise 11:…

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A: We know that, sin(90°+x) = cos(x) sin(90°-x) = cos(x)

Q: Prove the identity. csex- sinx cotx cosx

A: csc(x) = 1sin(x) cot(x)=cos(x)sin(x) sin2x + cos2x =1

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Q: prove the identity cosx + sinxtanx= secx

A: The given identity,cosx+sinx tanx=secx

Q: Verify the identity. sin (7x) - sin (3x) = - cot (5x) cos (7x) - cos (3x) Start with the numerator…

A: As we know that; The trigonometric identities: 1). sinA-sinB=2cosA+B2sinA-B22).…

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A: Basic question of trigonometry.

Q: Verify the identity. 9 cos(sin ¹ x) = √81 - 81x² = 8 = x = . Thus, Let 8 = sin-¹ x = sin 8 = x 9…

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Q: Find cos if sin = 1/2 terminates in QII

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Q: sinx - cosx+ 1 sinx + 1 sinx + COSX - 1 COSX

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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: Verify the identity 2 tan α/2 = (sin2 α + 1 - cos2 α)/sin α(1 + cos α)

A: Verify the identity 2 tan α/2 = (sin2 α + 1 - cos2 α)/sin α(1 + cos α)

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Q: Verify the identity. 2 cos 3x sin x = 2 sin x cos x – 8 cos x sin3 x Working with the left-hand…

A: Using the product to sum identity