Question

sin A ( 1 + tanA ) + cos A ( 1 + cot A ) = sec A + cosec A

Answer 1

Given LHS:

sin A(1 + tan A) + cos A(1 + cot A).

$sin A(1 + \frac{sin A}{cos A} ) + cos A(1 + \frac{cos A}{sin A})$

$\frac{sin A(cos A + sin A)}{cos A} + \frac{cos A(sin A + cos A)}{sin A}$

$(sinA + cos A)(\frac{sin A}{cos A} + \frac{cos A}{sin A} )$

$(sin A+ cos A) ( \frac{sin ^2A + cos^2A}{sin A * cos A})$

$(sin A + cos A) (\frac{1}{sin A * cos A})$

$\frac{sin A}{sin A * cos A} + \frac{cos A}{sin A * cos A}$

$\frac{1}{cos A} + \frac{1}{sin A}$

secA + cosecA


LHS = RHS.


Hope this helps!