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Csc² 0 cot²0 sin² 0 = cos² 0

Csc² 0 cot²0 sin² 0 = cos² 0-example-1
User Pramodpxi
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2 votes

Answer:

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}

User Nagham
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