5. Prove the following Identity: sin(2x) 1+ cos(2x) tan(x)

Q: 48. Simplify a. 1/cos x b. 1/secx c. 1/tan x d. 1/sin x 1 sin³ x col² x sin x

A:

Q: liu cos? (x) 1- sin (x)

A: Formula used: Sin2x + cos2x = 1 a2 - b2 = (a - b)(a + b)

Q: Differentiate the given sin (x² +1) 2 X

A: Sin(x2+1) To differentiate the given function

Q: T (b) fo 6 sin 20 cos² 20 ӨР

A:

Q: 5. Use substitution to find S sin1º0 cos 0 d0.

A: We will find the integration.

Q: 20. Prove the following identity. Use proper form. sin (-x) cosx= sin2x_1 3.1 cot (-x)

A:

Q: Prove: Sin(x-pi/2) = -cosx

A:

Q: 2x, given tan x= 2 and cos x is less than 0

A: Given tan x = 2 and cos x < 0.

Q: 3 S (sin x)*.dx

A: Please refer the attached image for complete solution.

Q: Is the function f(x)=sin(3x)+cos(tan x) even, odd, or neither? Why?

A: Recall: A function f(x) is even if  f(x) =f(-x). A function f(x) is odd if f(x)=-f(-x)

Q: O Find the anfidanialtiner Sfaw da for fla)= 18 Cos (6x) 16- Sin? (6x) © fa) = ¿* (, +x) 9 + xe

A:

Q: Ex2: Use the identities 4 and 5 to prove that: cos(x- y)-cos(x+y) (a) sin x sin y = 2

A: Formula used -  cos(A-B) = cosA cosB + sinA sinB  cos (A+B) = cosA cosB - sinA sinB

Q: sin(tan x) cos²x Evaluate ·[³ dx.

A:

Q: Q57.a) Find if y=sin(tant) and t=cos(x) dx

A:

Q: 2 Cos4 Sin (sinz) de

A: Consider the integral  ∫cosxsin2sinxdx

Q: Verify the identity sin t - cos 2t = (2 sin t - 1)(sin t + 1).

A: sin t - cos 2t=(2sin t-1)(sin t +1)Formulascos 2t= 1-2sin2t

Q: The simplified form of cos²(x) sin(x) + sin(1) is: Select one: a. sin(x) b. None of these c. cos(x)…

A:

Q: Evaluate [ sin” (tanx) x² I= So dx

A: Given, Integral  And according to lobachevsky integral formula

Q: tan(cos-1(x/4))

A: We will consider a right triangle where adjacent= x and hypotenuse= 4 In this triangle

Q: Find a sin²(x) dr. 16 +1 R

A:

Q: What are the two formulas for tan (A/2)

A: tanA2

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.