Find the identical expression for the following. ​sin x(sec x- cot x) A. sec x  B. cotx-sinx c. cosx d. tan x e. tan x- cos x

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A: The given integrals are; 7. ∫tan2x1+sin2xcos2xdx8.∫-134x-5dx

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A: Solution ) We know that  1) 1 + tan2x = sec2x 2)Sec x = 1/ cosx 3)Cotx sinx     [ cotx = cosx/sinx]…

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: 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

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

Q: 15. Use your identities for the following: sec(r)- 2V3 tan(x)< 0. Find sin(x) and cot(x) 3 а.

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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: 4. у%3D х?sinx + 2xcosx — 2sinx 5. g(t) = tan(t – sin2t)

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Q: Rewrite the following expression in terms of the given functions. 1 cos x and sin x tan X+ cot x

A: We have to Express

Q: For 180° < 0 < 270°, which of the primary trigonometric functions may have negative values? O tan 0…

A: Solution:

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Q: The following is equivalent to the choices below except | (tan (x)+ 1) dx 1 dx cos? (x) sec (x) dx…

A: Please refer the attached image for complete solution. THANK YOU.

Q: Evaluate the following expression when x is π/6. Use exact values. cos( x + pi/2)

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Q: d) Verify the identity sin 0 tan 2, 1+ cos e

A: To prove:

Q: Which of the following is equivalent (cos x + sin x)(cos x – sin x) 1. sin? 2x

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Q: 3. Mark was tasked with finding the exact value of tan(x+y) given that sin x = where -<x n and cos y…

A: Given that, sinx=725  and cosy=45

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Q: 11) Simplify the following: sec(x)csc(x)cos(x) A) 1 C) csc(x) B) sec(x) D) cot(x)csc(x)

A: Trigonometry

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A: We have to find the integral.

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

A: Here is the solution:

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: 1. Determine the sign (+ or -) that yields the correct formula for the following -(sinx + cos x) =+…

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Q: Verify the following identities. (sin x + cos x) = 1+sin 2x а. b. sec? x•tan? x + sec? x = sec* x 2x…

A: Given, The identities  a sinx+cosx2=1+sin2x b sec2x.tan2x+sec2x = sec4x We have to verify the…

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

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A: Given: (a)  sincos−122=?(b)  seccos−112=?

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A: To prove : tan2x - sec2xcos x = -sec x

Q: For 180° < 0< 270°, which of the primary trigonometric functions may have negative values? O cos 0…

A: The given angles 180°&lt;theta&lt;270°. We have to find which of the options have a negative value…

Q: 4. y = x'sinx + 2xcosx – 2sinx 5. g(t) = tan(t – sin2t)

A: In first questions use product rule of differentiation. And 2nd question use chain rule...

Q: Solveme of the following identities... tan? x - sin? x = sin? x tan2 x sinx + sinx cot x = csc x

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Q: Perform the indicated operation and simplify. 1. 1 sin t 1 Cos t tan t + sec t

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Q: B) If E-o(sin x)2" 2 tan x then find the value of x. 00 %3D

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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: Find, correct to six decimal places, the root of the equation cos x = x

A: To find :                          The root of the equation cos x = x up to six…

Q: 12. Verify the following trigonometric identities. tan (x) sin (2x) = 2 – 2 cos (x)

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Q: Evaluate the following 2 sin (x) -dx 1+ cos (x)

A: I = ∫0π/2sin(x)1+cos(x)dxI = ?

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Q: Use the following information to determine sin(2x). cos(x) 2 and tan(x) is positive Answer sin(2x) =

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.