Question

Question 4
Write ‘True’ or ‘False’ and justify your answer in each of the following:​​​​​​​
$\sqrt{(1-co{s}^2\theta )se{c}^2\theta }=tan\theta$

Answer 1

The statement is true.

$\sqrt{(1-co{s}^2\theta )se{c}^2\theta }=\sqrt{si{n}^2\theta .se{c}^2\theta }\lfloor \because si{n}^2\theta +co{s}^2\theta =1\rfloor$

$=\sqrt{si{n}^2\theta .\frac{1}{co{s}^2\theta }}=\sqrt{ta{n}^2\theta }[\because sec\theta =\frac{1}{cos\theta },tan\theta =\frac{sin\theta }{cos\theta }]$