Question

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

Answer 1

Explanation:

Taking left hand side:

`(1+tan\ x)/(sin\ x+cos\ x)\\=(1+(sin\ x)/(cos\ x) )/(sin\ x+cos\ x)\\=((cos\ x+sin\ x)/(cos\ x) )/(sin\ x+cos\ x)\\=(cos\ x+sin\ x)/(cos\ x) * (1)/(sin\ x+cos\ x)\\=(1)/(cos\ x)`

1/cos x is equal to sec x.

So,

`(1)/(cos\ x) = sec\ x`

Hence proved ..