Question

prove that the following identities, using half angle formula holds.
a. sin2(x/2) = CSC x - cot x/2csc x


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Answer 1

Step-by-step explanation:

The Pythagorean Identities are based on the properties of a right triangle.

cos2θ+sin2θ=1

1+cot2θ=csc2θ

1+tan2θ=sec2θ

The even-odd identities relate the value of a trigonometric function at a given angle to the value of the function at the opposite angle.

tan(−θ)=−tanθ

cot(−θ)=−cotθ

sin(−θ)=−sinθ

csc(−θ)=−cscθ

cos(−θ)=cosθ

sec(−θ)=secθ

The reciprocal identities define reciprocals of the trigonometric functions.

sinθ=1cscθ

cosθ=1secθ

tanθ=1cotθ

cscθ=1sinθ

secθ=1cosθ

cotθ=1tanθ

The quotient identities define the relationship among the trigonometric functions.

tanθ=sinθcosθ

cotθ=cosθsinθ