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

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Q: Evaluate the exact value of sin tan-()

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

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

Q: Evaluate cos tan Vx² + 1

A: We have to evaluate the given trigonometric function.

Q: Find an alternative form in terms of x for each of cos(sin- 1 x) and tan(sin- 1 x).

A: Let us make a triangle with opposite = x and hypotenuse=1 , because sin theta= opposite/hypotenuse…

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

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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: 4 Evaluate tan sin

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Q: prove sin2 a/2=csc a-cot a/2 csc a

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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,…