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प्रश्न
Prove that `(cot A - cos A)/(cot A + cos A) = (cos^2 A)/(1 + sin A)^2`
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उत्तर
`(cot A - cos A)/(cot A + cos A) = (cos^2 A)/(1 + sin A)^2`
L.H.S. `(cot A - cos A)/(cot A + cos A)`
= `(cos A/sin A - cos A)/(cos A/sin A + cos A)`
= `(cos A(1/sinA - 1))/(cos A(1/sin A + 1))`
= `(1/sin A - 1)/(1/sin A + 1)`
= `(1 - sin A)/(1 + sin A)`
= `(1 - sin A)/(1 + sin A) xx (1 + sin A)/(1 + sin A)`
= `(1 - sin^2 A)/(1 + sin A)^2`
= `cos^2 A/(1 + sin A)^2`
= R.H.S.
Hence Proved.
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tan2A − sin2A = tan2A · sin2A
Prove the following identities:
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Prove that `(tan(90 - θ) + cot(90 - θ))/("cosec" θ) = sec θ`.
Complete the following activity to prove:
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= `cosθ/sinθ + square/cosθ`
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= `1/(sinθ xx cosθ)` ....... ∵ `square`
= `1/sinθ xx 1/cosθ`
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∴ L.H.S. = R.H.S.
