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