Question

Help me verify the trig identity in terms of sin and cos

Answer 1

Given:

a trigonometric equation is given as below

`sin^2\theta(csc^2\theta+sec^2\theta)=sec^2\theta`

Find:

we have to vwerify the given identity.

Step-by-step explanation:

we will verify the identity as following

`\begin{gathered} L.H.S=sin^2\theta(csc^2\theta+sec^2\theta) \\ =sin^2\theta((1)/(sin^(^2)\theta)+(1)/(cos^2\theta))\text{ }(Since\text{ }csc\theta=(1)/(sin\theta)\text{ }and\text{ }sec\theta=(1)/(cos\theta)) \\ =sin^2\theta*(1)/(sin^2\theta)+sin^2\theta*(1)/(cos^2\theta) \\ =1+tan^2\theta\text{ }(because\text{ }(sin\theta)/(cos\theta)=tan\theta) \\ =sec^2\theta=R.H.S \end{gathered}`