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प्रश्न
Prove that `(1 + sec A)/(sec A) = (sin^2A)/(1 - cos A)`.
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उत्तर
L.H.S. = `(1 + sec A)/(sec A)`
= `1/(sec A) + (sec A)/(sec A)`
= cos A + 1
= `(1 + cos A) xx (1 - cos A)/(1 - cos A)`
= `(1 - cos^2A)/(1 - cosA)`
= `(sin^2A)/(1 - cosA)` ...`[(∵ sin^2A + cos^2A = 1),(∴ 1 - cos^2A = sin^2A)]`
= R.H.S.
∴ `(1 + sec A)/(sec A) = (sin^2A)/(1 - cosA)`
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