
Andy C. answered 05/16/18
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Math/Physics Tutor
(cot x)^2/(csc x + 1) = (1 - sin x)/sin x
Left hand side:
denominator is:
1/sinx + 1 = (1 + sinx)/sin x
The reciprocal is sin x / (1 + sinx)
The numerator is cot x^2 = (cosx)^2 / (sinx)^2
= ( 1 - (sinx)^2)/(sinx)^2
= ( 1 + sinx)(1-sinx)/(sinx)^2
Multiplying them together:
( 1+ sinx)(1-sinx)/(sinx)^2 * sinx/(1+sinx)
(1-sinx)/sinx <--- factor of 1+sinx cancels, as does 1 factor of sine
This expression is identical to the right hand side, which concludes the proof