Prove the identity (sin x + cos x)? – sin(2x) =1

Q: Verify that the equation is an identity. 2 sin x tan 2.r = 2 cos x - sec x

A:

Q: in−1(x) + cos−1(x) =  ? 2

A: Given that : The equation is sin-1 (x) + cos-1 (x) = π2 .

Q: Prove the identity. 3 sin(x - y) 3 tan x - 3 tan y = cos y cos x

A:

Q: Prove the identity. +x + sin 6. sin = cos x

A: Given, We have to prove the identity sinπ6+x+sinπ6-x=cosx

Q: Prove the identity: sin? x + cos² x = 1, using the Mean Value Theorem.

A:

Q: Prove the identity. Cos(x− 90°) − Cos( x + 90°) = 2 sin x

A: We will use the formulas: cos(A-B)=cosAcosB+sinAsinBcos(A+B)=cosAcosB-sinAsinB

Q: Prove the identity sin(-0)- cos (+0)

A:

Q: 5. Verify the identity: sin(x- y)cos y+cos(x– y)sin y = sin x

A: Explanation of the solution is given below.....

Q: Prove the identity (sin x - cos x)2 = 1 - sin 2x

A:

Q: Prove the identity: cos(x + y)cos(x – y) = cos?x – sin²y

A:

Q: 2 cos" (x)–sin°(z)+1 cos(x) 3 cos(x) 10. Verify the following identity, justifying each step.

A:

Q: Prove the identity sin x cos²x+ sin?x algebraically and CSC X determine the non-permissible values…

A:

Q: Prove the identity 1/Cos X - 1/Sec X = Tan X * Sin X

A:

Q: snip

A: Our Aim is to establish the identity given below:-1-sinθcos (θ)=cos (θ)1+sinθ-(i)

Q: Verify the identity: cos(3x) cos(x)(1 – 4 sin? (x))

A: we have to verify the given identity. the solution is following

Q: Prove the identity. sin'x cos'x= (cos'x- cos"x) sin x

A:

Q: (a) Prove that Sin-1x  + Cos-1 x  = π/2 .(b) Use part (a) to prove Formula 6.

A: a) We have to prove sin-1x+cos-1x=π2 Let sin-1x=θ                                     ⋯⋯1…

Q: Prove the identity: (sin x – cos x)(sin x + cos x) = 2 sin² x – 1

A: As value of cosθ and sinθ revolves around +1 to -1 , they take different values depending on the…

Q: 3. Prove that the identity is true. sin*t - costt tan-t– 1 cos't

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Prove the identity  Cos x/1+sin x + Cos x/ 1-sinx = 2sec x

A:

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

A:

Q: Another form of sec x dx cos x 1- sin²x b. Use the identity in part (a) to verify that 1. |1 + sin…

A: a) we have to verify the identity sec(x)=cos(x)1-sin2(x)Consider, RHS=cos(x)1-sin2(x)we…

Q: 3. Prove that sin (x+÷) = cos x is an identity.

A:

Q: Prove: sin? x 2 cos“ = cos 2-2cos x

A: We will use basic properties of trigonometric ratios

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

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

Q: Prove that: Sin'x+ cosx=I

A:

Q: Use an identity to solve the equation cos 2x = cos x on the interval [0, 2π).

A: Given:cos2x=cosx on the interval [0,2π)Formula:cos2x=cos2x-sin2xsin2x=1-cos2x

Q: prove the identity  sin(x) + sin(3x) = 4 sin(x) cos2(x)

A:

Q: PROVE that sin x = v1 – cos² x is NOT an identity.

A: Topic:- trigonometry

Q: Verify the identity : sin 4t = 4 sin t cos3 t - 4 sin3 t cos t

A: Verify the identity : sin 4t = 4 sin t cos3 t - 4 sin3 t cos t

Q: 4. Establish the identity using the sum and difference formulas: sin (m – 0) = sin 0

A:

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

A:

Q: Prove identity: 4 sin x cos x (1 – 2 sin? x) = sin(4x)

A:

Q: 4. Verify the following identities: a. sin 3x = 3 sin x-4 sin3 x b. 1+ cos 10x = 2 cos? 5x %3D

A:

Q: 24. Prove the identity 1 – (sin x – cos x)2 = sin 2x

A:

Q: Prove the identity. TT COS +0+ -sin 0

A:

Q: Prove that, cos20 + sin?0 = 1

A: Let a, b and c be the lengths of right angled triangle. Then by definition,

Q: Prove the identity. sin x 1+ cos x 1- cos x sin x

A:

Q: Verify the following identities: a. sin 3x = 3 sin x-4 sin x b. 1+ cos 10x = 2 cos 5x %3D

A:

Q: Prove that cos(sin-x) = /I– x².

A: Given: sin-1x=cos-11-x2

Q: Find z where z = sin (æ²) cos (4²) COS

A: The given function is z=sinx2 cosy2.

Q: Verify the trigonometric identity sin(z - 1/2) = - cos(z)

A:

Q: Prove the identity. 3 sin(x – y) cos y cos x 3 tan x - 3 tan y

A: Given that  3tanx-3tany=3sin(x-y)cosycosx We need to verify the given identity.

Q: Verify the identity. 1- sin x + COs X 1 + sin x + cos X COS X | sin x + 1

A:

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

A:

Q: 7. Prove the identity. – sin 3 TT -x= 0 2 sin +x 2

A:

Q: Verify the identity : cos (x - 5π/4) = - √2(cos x + sin x)/2.

A: Consider the given expression as, cosx-5π4

Q: Prove the identity sin30 cos 30 = 2 cos e sin 0

A: The given equation is sin3θsinθ-cos3θcosθ=2 the objective is to prove the identity. the formula for…

Q: Verify the identity. (1 – cos"(x)(1 + cot*«») = (1 - cos (x)(1 + cot°») - sin°C«) - 1 + sin (x) =…

A: Solved below