Simplify each expression to 1, - 1 or either A. Tanxcot(-x) B. Cos(x) cos(-x) C. Sin(-x) csc(-x)

Q: Find the exact value of the expression. -1 15 cos tan 8

A: The given expression is costan-1158. It is known that, cosarctanx=1+x21+x2.

Q: 51. Write csc x in terms of cos x.

A: sin2x +cos2x =1 ⇒  sin(x )=±1-cos2(x). csc(x) =1sin(x)

Q: Find the exact value of each expression, if it is defined. A. sin-l1 B. cos-1(-1) C. sin-1 2 D.…

A: To find the value of inverse trigonometric functions.

Q: Write the given expression in terms of x and y only. tan(sin-(x) + cos-(v))

A:

Q: Use the addition and subtraction formulas to simplify the expression. cos(x +y) cos(x - y)

A:

Q: Simplify the following expressions: cos 20 a. sin 8+cos 0 tan 2x b. tan x C. sin 2x tan-

A: a) The given expression is, cos 2θsinθ+cosθ. Simplify the expression as shown below. cos…

Q: Enter a simplified algebraic expression for the expression. X, cos tan %3D

A:

Q: Rewrite the expression as an algebraic expression in x. cos(sin−1(x))

A:

Q: Match each expression with the appropriate formula that would be used for simplification. sin 8x +…

A: Solution:-

Q: Use the above to evaluate x sin(x) ap: - 72

A: c) Given that, quadrature formula ∫01x1-x2fxdx=∑i=0nai fxi To find: ∫01x sinx1-x2dx

Q: Write the given expression as an algebraic expression in x. sin(2 tan-'(x))

A: Trigonometric

Q: Write the given expression as an algebraic expression in x. tan(2 cos-1(x))

A: According to the question, we have to solve the expression tan2 cos-1x and write as an algebraic…

Q: Find the values sin2X, cos2X, and tan2Xfor the given value of X, cotX = 4/3; 180o < X < 270o

A:

Q: Simplify the expression. co x+10 cos x + 25 COSX +5 COS X+ 5 O cOs X -5 sin x + 5 cosx-5 1.

A:

Q: Use the addition and subtraction formulas to simplify the expression. cos(x+y) cos(x - y)

A: Given,            cosx + y cosx - y

Q: Simplify the expression V16 - x2 as much as possible after substituting 4 sin(0) for x. (Assume 0° <…

A: Given query is to simplify the expressions by substituting x.

Q: Write an equivalent algebraic expression that involves x only.      tan (cos- 1 x)

A: Evaluate tancos-1x       ...(1)

Q: 2. Simplify the expression: cos (x+)+ cos (x (x%) (i +*) =

A:

Q: Use substitution to rewrite 4 cos^2 x=4

A:

Q: Write cos x in terms of tan x.

A: tanx= sinx/cosx Squaring on both sides We get, tan^2(x)=sin^2(x)/cos^2(x) tan^2(x)=…

Q: Verify the identity by transforming the lefthand side into the right-hand side.

A: sinθ+cosθcosθ=1+tanθwe have to prove left hand side equals to right hand side so there are two…

Q: Simplify the following expression: sin(180°+x) tan(180°-x) tan 45° cos(360°-x)

A:

Q: Simplify the expression √4 − x^2( as much as possible after substituting 2 sin  for x.

A:

Q: If 0 = 315°, find the exact value of each expression below. (a) cos (-0) = (b) cos e = 0 mun (c) 2…

A:

Q: Verify the following identity. sin x+ cos 2x = cos To transform the left side into the right side,…

A: Trigonometric identities are mathematical equations that stay valid for right-angled triangles.…

Q: Rewrite the expression cos (0) without using any powers of sin or cos.

A: We have to rewrite the expression cos4( θ) without using the powers of sin or cos .

Q: Simplify the expression.  cos(2tan -1     x)

A: we have to simplify the expression. cos(2tan -1x)

Q: Evaluate the following expressions. sin (tan-(1)) cos (tan-(0))

A: We need to evaluate the given expressions sintan-11costan-10

Q: Write the expression as a Single trigonometnic furction. cos 6x cos4x Sin6x Sin4x a Cos 12x b. Sin…

A: Explanation of the answer is as follows

Q: Simplify each of the following fully: 3.3.1 sin(180° – x).cos (x-180').tan x cos(90° – x).sin(360° +…

A: Given expression is sin180°−xcos2x−180°⋅tanxcos90°−x⋅sin360°+x. We have to simplify the given…

Q: Write an equivalent algebraic expression that involves x only  cosec   ( sin  -1 1/ x)

A: Given: The expression cosecsin-11x, To find: The algebraic expression equivalent to given expression…

Q: Write the given expression as an algebraic expression in x. sin(2 tan-¹(x)) X

A:

Q: Write the given expression as an algebraic expression in x cos(2 tan−1(x))

A: Given:

Q: Find the exact value of the expression below. tan() + tan() 2T 1 – tan() +tan( 15

A:

Q: Find the exact value of the following expression. 5x tan +3) 6 4

A: For the value of tan(5π/6 + π/4) . . . (1)   We use the formula  tan(a+b)=(tana + tanb)/(1-…

Q: Rewrite the expression, cos x/(1 + sin x) + tan x; cos x  in terms of the given function or…

A: Rewrite the expression, cos x/(1 + sin x) + tan x; cos x  in terms of the given function or…

Q: Write the expression cos (2 sin'x) as an algebraic expression in x, where (-1< x <1). Select one:…

A:

Q: Write the given expression as an algebraic expression in x. tan(2 sin-1(x))

A: To solve the following problem

Q: Simplify: 1+ cos 2x. 2 cot2 x

A:

Q: Simplify the expression :  sec x cos x + cos x − 1/sec x  using basic identities

A: The basic identity is:cosx=1secx or secx=1cosx

Q: Write an equivalent algebraic expression that involves x only.    sin (cos- 1 x)

A: Given algebraic expression is sincos-1x. To write an equivalent algebraic expression that involves x…

Q: Simplify the expression. 2 cos x + 16 cos x + 64 cos x + 8

A:

Q: Evaluate the following expression when x is π/6. Use exact values. sin 2x

A:

Q: Apply the sum and difference identities to find the exact value of the given expression in terms of…

A: Given expression

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.