Question

Prove the identity cot^2x/cscx+1=1-sinx/sinx

Answer 1

cot²x/csc+1
=(csc²x-1)/(csc+1)

=((1/sin²x)-1)/((1/sinx)+1)

=((1-sin²x)/sin²x)/((1+sinx)/sinx)

=(1-sin²x)/(1+sinx)

=(1+sinx)(1-sinx)/sinx(1+sinx)

=(1-sinx)/sinx

Answer 2

The given trigonometric identity is proved to be true.

What is a trigonometric identity?

"Trigonometric identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation. "

Given, cot² x / (cosec x + 1)

= (cosec² x - 1) / (cosec x + 1)

= (cosec x + 1) (cosec x - 1) / (cosec x + 1)

= (cosec x - 1)

= (1 / sin x) - 1

= (1 - sin x) / sin x

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