Prove the following equations are identities for all permissible values of x, by manipulating only the left side of each equation. sin x + tan x sin x 1+ secx 1 1 1+sinx 1-sinx = 2 sec² x

Q: VERIFY THE IDENTITIES

A:

Q: Is (1-sin x) not the same as (sin x - 1)?

A: (x - y) is not same as (y - x), whereas  (x - y) = - (y - x)

Q: tan x -1 X 1+ x?

A: To evaluate the given

Q: Evaluate cos tan Vx² + 1

A: We have to evaluate the given trigonometric function.

Q: 2. sin 2x 1 - sin² x = 2 tan x

A: Aim: To show that sin(2x)1-sin2(x)=2tan(x)

Q: What is sin x

A: To explain about sin x

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

A: sinx1+cosx=sinx1+cosx×1-cosx1-cosx=sinx1-cosx1-cos2x     ∵a+ba-b=a2-b2=sinx1-cosxsin2x…

Q: Verify the identity:

A:

Q: Find sin 5, given that sin x = 2 i and 0<x<5.

A: Here  sin x=14⇒cos x=1-sin2x              ⇒cos x=1-116              ⇒cos x=154 Now, sin2x2=1- cos x2…

Q: If z = tan X 2 then sin x =

A:

Q: Verify the identity: tan x + 1/tan x = 1/(sin x cos x)

A: To verify: tan x+1tan x=1sinx. cosx

Q: Verify the identity: [sin 2x + (sin 3x + sin x)]/[cos 2x + (cos 3x + cos x)] = tan 2x

A: Consider the identity, sin2x+sin3x+sinxcos2x+cos3x+cosx=tan2x To apply the trigonometric identity,…

Q: Find all values of such that sin2x=sinx and 0&lt;=x&lt;=2pie

A: Given equation is Now, we use the identity sin2x=2sinxcosx,