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Question
Prove the following trigonometric identities.
`tan theta - cot theta = (2 sin^2 theta - 1)/(sin theta cos theta)`
Solution
We have to prove `tan theta - cot theta = (2 sin^2 theta - `1)/(sin theta cos theta)`
We know that. `sin^2 theta + cos^2 theta - 1`
So,
`tan theta - cot theta = sin theta/cos theta - cos theta/sin theta`
`= (sin^2 theta - cos^2 theta)/(sin theta cos theta)`
`= (sin^2 theta - (1 - sin^2 theta))/(sin theta cos theta)`
`= (sin^2 theta - (1 - sin^2 theta))/(sin theta cos theta)`
`= (2 sin^2 theta - 1)/(sin theta cos theta)`
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