Question

Let to help me please....

Answer 1

Given LHS = sinA(1 + tan A) + cosA(1 + cot A)

 = sinA + sinA * tan A + cosA +  cosA * cotA

= $sin A + sinA * \frac{sinA}{cosA} + cos A + cosA * \frac{cosA}{sinA}$

= $sinA + \frac{sin^2A}{cosA} + cosA + \frac{cos^2A}{sinA}$

= $sinA + \frac{cos^2A}{sinA} + cosA + \frac{sin^2A}{cosA}$

= $\frac{sin^2A + cos^2A}{sinA} + \frac{cos^2A + sin^2A}{cosA}$

= $\frac{1}{sinA} + \frac{1}{cosA}$

= cosecA + secA.


LHS = RHS.


Hope this helps!