Question

1 + tan squared theta by 1 + sec theta is equal to sec theta prove it

Answer 1

hey mate! got ur answer hope it helps!!!

Answer 2

$1+\frac{\tan^{2} \theta}{1+\sec \theta}=sec \theta$, proved.

Step-by-step explanation:

L.H.S. $=1+\frac{\tan^{2} \theta}{1+\sec \theta}$

$=\frac{1+\sec \theta +\tan^{2} \theta}{1+\sec \theta}$

$=\frac{(1 +\tan^{2} \theta) +\sec \theta}{1+\sec \theta}$

$=\frac{\sec^{2} \theta +\sec \theta}{1+\sec \theta}$

Using trigonometric identity,

$1 +\tan^{2} \theta=\sec^{2} \theta$

$=\frac{\sec \theta(1+\sec \theta)}{1+\sec \theta}$

$=sec \theta$

=R.H.S., proved.