Which of the following is equivalent to [sin(-x) + cos(-x)]? 1 - 2sinxcosx O 1 O 1+ 2sinxcosx O sin'x - cos'x

Q: 4. Establish the identity: sec ar - secr sin2 = cos LIC HS O6Y

A: Establish the identity

Q: Cos x = Cos" x 1-

A: In this question we have to prove cosx=cos-1x.

Q: What is the exact value of 2sin(x/2) * cos(x/2) if sin of x = 3/5 and cos of x = 4/5 ?

A: To determine the exact value of the expression.

Q: Verify the identity. sin 0-1 tan 0- sec 0 %3D cos e

A: Here we use basic identities of trigonometric ratios.

Q: Verify the identity: (cos 4x - cos 2x)/(sin 2x - sin 4x) = tan 3x

A:

Q: 5. Evaluate π/3 π/6 cos3 x sin−2 xdx.

A: 5.Solution…

Q: Verify the identity.

A: We have  cosx-5π2=sinx   It is known that cosA-B=cosAcosB+sinAsinB   Consider LHS:…

Q: Prove the identity. cos(3x) − cos^3 x = − cos x sin^2 x − sin x sin(2x)

A:

Q: * Prove: sin x = cos COS 2- 2cos x

A:

Q: Verify the identity. cos x = sin x sin 2x + cos x cos 2x

A: we have to verify the identity

Q: -sin (In x?)ecos² (In x) dx 100x2-x2e2 cos (In x)

A:

Q: Verify the identity sec-1 x = cos-1(1/x), for x ≠ 0.

A: According to the question, we have to verify the identity sec-1x=cos-11x. As the above function is…

Q: Suppose cos x = - , where n < x < * . Find the exact value of cos(x – 4) . COS

A: cos(A-B)=cos A cos B+ sin A sin B

Q: 1- sin2x/1+cos x=cos x. Verify the identity

A: The given identity:

Q: To evaluate sin42x cos 2x dx , the identities to be used is/are: sin22x = 1- cos?2x В cos²2x = 1-…

A: Check the identities

Q: Find the value of cos(4x) if = 4. 3 1-cos(x)-sin(x)

A: trigonometry

Q: To evaluate sin*2x cos 2x dx , the identities to be used is/are: sin4x, 1- cos4x A 2 B cos²2x=1-…

A: Solution:-  This types of trignometric integrals can be solve by reduction formula of integral.

Q: 46 a Show that cos x+ =-sinx. = -sinx. d" (cosx) = cosx + drn b Prove that

A:

Q: Verify the identity: 4 cos x cos 2x sin 3x = sin 2x + sin 4x + sin 6x

A: We have to verify the identity: 4cosxcos2xcos3x=sin2x+sin4x+sin6x We know that…

Q: Establish the identity. (5-) - sin cos 0 %3D

A: Given,          sinπ2-θ=cosθWe know that,           sinA-B=sinAcosB-cosAsinB

Q: Prove sin (90◦+x) + sin (90◦−x) = 2 cosx

A:

Q: 21 Prove the identity.cos x (1 ²x) 2 2. - sin sec X,

A: Consider the given identity cos2x1-sec2x=-sin2x.

Q: Which is equal to (sin⁡x+cos⁡x)^2+(sin⁡x−cos⁡x)^2 using identities?

A: Now we use identity  Sin2x +cos2x =1 And formula (a+b)2= a2 +b2 + 2ab  (a-b)2 = a2 + b2 - 2ab

Q: - 3in 2 X sin X- COSX

A:

Q: 4. Prove that cos(sin¬1 x) = /1 – x².

A: cos(sin-1x)=1-x2⇒sin-1x=cos-1(1-x2)Let y=sin-1x                               (1) ⇒siny=x…

Q: Prove ONE of the follow sin x+ cos 2x-1 tan x %3D a) cos x-sin 2x

A:

Q: 16. Establish the identity: os 0)² + (sin 0- cos 0)2 = 2 %3D

A: We need to establish the identity  (sinθ+cosθ)2+(sinθ-cosθ)2=2

Q: Prove the identity. s (xxy) sinx- sin (x-y) cosx= siny cos

A:

Q: Verify the identity: sin (3π/2 - x) = -cos x

A: To prove  sin (3π/2 - x) = -cos x

Q: Prove the below cos' x sin 3x + sin' x cos 3x 3 sin 4x 4 II

A: Simplification of trigonometry function

Q: verify sin2(x)+cos2(x)=1

A:

Q: Prove the identity. + sin 3 cos x- cosx

A:

Q: 7. Show that sin (+ x) = -cosx.

A:

Q: 05 of the ac 42. Use the identity sin 2x = 2 sin x cos x to find the derivative of sin 2.x. Then use…

A: Find the derivative sin2x

Q: To evaluate sin42x cos 2x dx , the identities to be used is/are: A cos?2x=1– sin2x 1+ cos4x & 2…

A:

Q: Simplify sin “ z – cos“ æ O 2cos (x) - 1 O 2sin*(x) - 1 O 1+ 2sin*(x) O 1+ 2cos (x)

A: Using trigonometric identities.

Q: Prove: sin² x + 2 cos²x − 1 = cos²x -

A:

Q: The suitable substitution to evaluate | sin 4(x+2) dx is None (1- cos8(x +2)] [1- cos4(x + 2)]…

A: Given that: ∫sin24(x+2)dx

Q: Verify the identity. sin 5x + sin 3x 2 cos x 4 sin x cos3 x - X – 4 sin x cos x 3.

A:

Q: The suitable substitution to evaluate | sin² 4(x + 2) dx is None O A. - cos8(r +2)] [1- cos4(r+ 2)]…

A:

Q: cosh(3i)is equal to O -cos3 O cosh 3 cos 3 O sin 3

A:

Q: prove the identity sin^2xcos^2x+cos^(4)x=(1-sinx)(1+sinx)

A:

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…

A:

Q: Show that 4 sin x cos 2x + 3 = 8 cos %3D x.

A: We will use the formula of cos 2x and other formulas of trigonometry to prove left hand side is…

Q: 1- cos 0 1+ cos 0 sin 0

A:

Q: Show that 1 − cos x = x2/2 with an error less than 0.003 for |x| &lt; 1/2.

A: Given: 1-cos x =x22;    |error|&lt;0.003Formula:  The…

Q: Verify the identity. sin 3x 1 = 2 cos x- %3D sec x 2 - sin 2x

A: Given: Verify the identity sin3xsin2x=2cosx-12secx for verifying given identity we solve left hand…

Q: To evaluate sin 2x cos 2x dx , the identities to be used is/are: sin4x , 1+ cos4x A 2 2 ® cos?2x=1-…

A: To find The identities to be used.