Question

Verify the identity. 1+tan x/sin x + cos x= sec x

Answer 1

Step-by-step explanation:

Taking left hand side:

$\frac{1+tan\ x}{sin\ x+cos\ x}\\=\frac{1+\frac{sin\ x}{cos\ x} }{sin\ x+cos\ x}\\=\frac{\frac{cos\ x+sin\ x}{cos\ x} }{sin\ x+cos\ x}\\=\frac{cos\ x+sin\ x}{cos\ x} * \frac{1}{sin\ x+cos\ x}\\=\frac{1}{cos\ x}$

1/cos x is equal to sec x.

So,

$\frac{1}{cos\ x} = sec\ x$

Hence proved ..