Given:
a trigonometric equation is given as below
[tex]sin^2\theta(csc^2\theta+sec^2\theta)=sec^2\theta[/tex]
Find:
we have to vwerify the given identity.
Explanation:
we will verify the identity as following
[tex]\begin{gathered} L.H.S=sin^2\theta(csc^2\theta+sec^2\theta) \\ =sin^2\theta(\frac{1}{sin^{^2}\theta}+\frac{1}{cos^2\theta})\text{ }(Since\text{ }csc\theta=\frac{1}{sin\theta}\text{ }and\text{ }sec\theta=\frac{1}{cos\theta}) \\ =sin^2\theta\times\frac{1}{sin^2\theta}+sin^2\theta\times\frac{1}{cos^2\theta} \\ =1+tan^2\theta\text{ }(because\text{ }\frac{sin\theta}{cos\theta}=tan\theta) \\ =sec^2\theta=R.H.S \end{gathered}[/tex]
