Question

When is an equation called identity prove the trigonometric identity 1+tan^A=sec^A

Answer 1

An equation is called an identity when it holds true for any value of the variable. 

Answer 2

$1+\tan^2 A=\sec^2 A,$, proved.

Step-by-step explanation:

Prove that, $1+\tan^2 A=\sec^2 A$

L.H.S. =$1+\tan^2 A$

$=1+\dfrac{\sin^2 A}{\cos^2 A}$

[ ∵ $\tan^2 A=\dfrac{\sin^2 A}{\cos^2 A}$]

Taking LCM, we get

$=\dfrac{\cos^2 A+\sin^2 A}{\cos^2 A}$

$=\dfrac{1}{\cos^2 A}$

[ ∵$\sin^2 A+\cos^2 A=1$]

$=\sec^2 A$

=R.H.S.

Hence, $1+\tan^2 A=\sec^2 A,$, proved.