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प्रश्न
Prove the following trigonometric identity.
`cos^2 A + 1/(1 + cot^2 A) = 1`
उत्तर
L.H.S. = `cos^2 A + 1/(1 + cot^2 A)`
= `cos^2 A + 1/("cosec"^2 A) ...[1 + cot^2A = "cosec"^2 A]`
= `cos^2 A + sin^2 A ...[1/("cosec" A) = sin A]`
= `cos^2 A + sin^2 A`
= 1 (R.H.S.) ...`[sin^2 A + cos^2A = 1]`
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Activity:
L.H.S = `square`
= (sin2A + cos2A) `(square)`
= `1 (square)` .....`[sin^2"A" + square = 1]`
= `square` – cos2A .....[sin2A = 1 – cos2A]
= `square`
= R.H.S
