Question

1+sin theta + cos theta / cos theta = sec theta +tan theta + 1​

Answer 1

on LHS divide numerator and denomination by cosA

ie, 1/cosA+sina/cosa+cosa/cosa whole divided by cosa/cosa

IE, seca+tana+1....

LHS=RHS

hence proved

Answer 2

Question :-

Prove that

$\frac{1 + \sin \theta + \cos \theta}{ \cos \theta} = \sec \theta + \tan \theta + 1$

Formula used :-

$\star \: \frac{1}{ \cos \theta} = \sec \theta \\ \\ \star \: \frac{ \sin \theta}{ \cos \theta} = \tan \theta$

Explanation :-

Taking left hand side,

$\implies \: \frac{1 + \sin \theta + \cos \theta}{ \cos \theta} \:$

split it into parts

$\implies \: \frac{1}{ \cos \theta} + \frac{ \sin \theta}{ \cos \theta} + \frac{ \cos \theta}{ \cos \theta}$

according to the given formula,

$\implies \sec \theta + \tan \theta + 1$

left hand side = right hand side

hence proved.