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Prove that `Sqrt(Sec^2 Theta + Cosec^2 Theta) = Tan Theta + Cot Theta` - ICSE Class 10 - Mathematics

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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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Solution Prove that `Sqrt(Sec^2 Theta + Cosec^2 Theta) = Tan Theta + Cot Theta` Concept: Trigonometric Identities.
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