Prove that ^2 (1+ ^2 )=1. complete the activity given below. Acti… - Vidyadip

Question

Prove that $\cos ^2 \theta \cdot\left(1+\tan ^2 \theta\right)=1$. complete the activity given below.
Activity:
$ \text { L.H.S }=\square$
$=\cos ^2 \theta \times \square \ldots . .\left[1+\tan ^2 \theta=\square\right]$
$=(\cos \theta \times \square)^2$
$=1^2$
$=1$
$=\text { R.H.S } $

✓

Answer

$\text { L.H.S. }=\cos ^2 \theta \cdot\left(1+\tan ^2 \theta\right)$
$=\cos ^2 \theta \times \sec ^2 \theta \quad \ldots . .\left[1+\tan ^2 \theta=\sec ^2 \theta\right]$
$=(\cos \theta \times \sec \theta)^2$
$=1^2$
$=1$
$=\text { R.H.S }$

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