Question

(cosec theta-cot theta)^2=(1-cos theta)/(1+cos theta)

Answer 1

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Answer 2

Please refer the above photograph for the used process.

KEY POINTS TO REMEMBER :-

☸️ Certain trigonometric relations like:-

$\cosec(x) = \frac{ 1 }{ \sin(x) } \\ \\ \cot(x) = \frac{ \cos(x) }{ \sin(x) }$

☸️ Trigonometric identities like :-
Sin²x + cos²x = 1


☸️ Certain Identities like :-

${(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy \\ \\ {(x - y)}^{2} = (x - y)(x - y) \\ \\ {x}^{2} - {y}^{2} = (x + y)(x - y)$

☸️ NOTE :- To solve these kind of problems, try to find out the relation and common ratios present in both LHS and RHS.

☸️ Easiest way to solve all these type of problems is to convert the ratios in sin and cos form and go for further calculation.

Thanks!