Question

Csc² 0 cot²0 sin² 0 = cos² 0

Answer 1

Explanation:

Given equation:

`\csc^2 \theta - \cot^2\theta -\sin^2\theta =\cos^2\theta`

To verify the given trigonometric equation, we can use the following trigonometric identities:

`\boxed{\begin{minipage}{5 cm}\underline{Trigonometric Identities}\\\\$\csc^2 \theta = 1 + \cot^2 \theta$\\\\$\cos^2 \theta + \sin^2 \theta = 1$\\\end{minipage}}`

Therefore:

`\begin{aligned}\csc^2 \theta - \cot^2\theta -\sin^2\theta &=(1+\cot^2\theta) -\cot^2\theta -\sin^2\theta \\&=1-\sin^2\theta\\&=(\cos^2\theta +\sin^2\theta) -\sin^2\theta \\&=\cos^2\theta \end{aligned}`