Question

(sin theta / cot a+cosec a) - (sin theta/cot a-cosec a)

Answer 1

METHOD-01

$LHS = \frac{sinA}{cotA+cosecA} - \frac{sinA}{cotA-cosecA}\\\\\\=\frac{sinA(cotA-cosecA)-sinA(cotA+cosecA)}{cot^2A-cosec^2A} \\\\\\=\frac{(cotA-cosecA)(cotA+cosecA)}{cot^2A-cosec^2A}\\\\\\=\frac{cot^2A-cosec^2A}{cot^2A-cosec^2A} \\\\\\=1 \\RHS$

METHOD-02

attached

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