Question

prove that Cos A * cot A /1+sin A = cosec A-1

Answer 1

Answer:

To prove : $\frac{cosA*cot A}{1+sinA}=cosec A-1$

LHS:

$\frac{cos A * cot a}{1+sinA}\\\\=\frac{cos A * \frac{cos A}{sin A}}{1+sinA}\\\\=\frac{cos A * cos A}{(1+sinA)sin A}\\\\=\frac{cos^2A}{(1+sinA)sin A} \\\\=\frac{1-sin^2A}{(1+sinA)sin A} \\\\=\frac{(1-sinA)(1+sinA)}{(1+sinA)sin A} \\\\=\frac{1-sinA}{sin A} \\\\=\frac{1}{sinA} - \frac{sin A}{sin A} \\\\= cosec A - 1$