Question

Sin theta+tan theta/cos theta= tan theta (1+sec theta)

Answer 1

Explanation

(sin theta +tan theta)/cos theta

=sin theta/cos theta +tan theta/cos theta

=tan theta+ tan theta ×1/cos theta

=tan theta + tan theta sec theta

=tan theta(1+sec theta)

Answer 2

Solution →

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

Let's take LHS →

$= \frac{sin \: \theta \: + \: tan \: \theta }{cos \: \theta}$

We can write it as →

$= \frac{sin \: \theta}{cos \: \theta} \: + \: \frac{tan \: \theta}{cos \: \theta}$

We know that →

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

$= tan \: \theta \: + \: tan \: \theta \: \times \frac{1}{cos \: \theta} \:$

$= tan \: \theta + tan \: \theta \times sec \: \theta$

Lets take $tan \: \theta$ common ,

$\boxed{= tan \: \theta(1 + sec \: \theta)}$

RHS !!

Hence Proved!!

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