Question

Verify the identity. (cos x/ 1+ sin x) + (1+ sin x/cos x) = 2 sec x​

Answer 1

Answer:

LHS

$\frac{cos x}{1+ sin x} + \frac{1+ sin x}{cos x} \\=\frac{cos2(x)+1+2sin(x)+sin2(x)}{cos(x)(1+sin(x)} \\= \frac{2+2sin(x)}{cos(x)(1+sin(x))} \\\\=\frac{2 (1 + sin(x))}{cos(x)(1+sin(x))} \\= \frac{2}{cos (x)} \\= 2 sec x$

= RHS PROVED

hope it helps :)