Question

Prove (1+sin/csc-cot)-(1-sin/csc+cot)=2(1+cot)​

Answer 1

`(1+sin)/(csc-cot)-(1-sin)/(csc+cot)=2(1+cot)\\\\\\\text{Proof from LHS }\rightarrow \text{ RHS}\\\\(1+sin)/(csc-cot)\bigg((csc+cot)/(csc+cot)\bigg)-(1-sin)/(csc+cot)\bigg((csc-cot)/(csc-cot)\bigg)\\\\\\(csc+cot+sin csc+sincot)/(csc^2-cot^2)+(-csc+cot+sincsc-sincot)/(csc^2-cot^2)\\\\\\(2cot+2sincsc)/(csc^2-cot^2)\\\\\\(2(cot+sincsc))/(1)\\\\\\2\bigg((cos)/(sin)+(sin\cdot1)/(sin)\bigg)\\\\\\2(cot+1)\\\\\\2(1+cot)=2(1+cot)`

LHS = RHS
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