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Question
Prove that `sqrt(sec^2 theta + cosec^2 theta) = tan theta + cot theta`
Solution
L.H.S = `sqrt(sec^2 theta + cosec^2 theta)`
`= sqrt(1/(cos^2 theta) + 1/(sin^2 theta))`
`= sqrt((sin^2 theta + cos^2 theta)/(cos^2 theta sin ^2 theta))`
`= sqrt(1/(cos^2 theta sin^2 theta))`
`= sqrt(1/(cos^2 theta) xx 1/(sin^2 theta))`
`= sqrt(sec^2 theta xx cosec^2 theta)`
`=sec theta xx cosec theta`
R.H.S = `tan theta + cot theta = (sin theta)/(cos theta)+ cos theta/sin theta = (sin^2 theta + cos^2 theta)/(cos theta sin theta) = 1/cos theta xx 1/sin theta = sec theta xx cosec theta`
Thus L.H.S = R.H.S
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