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प्रश्न
Prove the following identities:
`1 - cos^2A/(1 + sinA) = sinA`
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उत्तर
L.H.S. = `1 - cos^2A/(1 + sinA)`
= `(1 + sinA - cos^2A)/(1 + sinA)`
= `(sinA + sin^2A)/(1 + sinA)`
= `(sinA(1 + sinA))/(1 + sinA)`
= sin A = R.H.S.
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tan2θ – sin2θ = tan2θ × sin2θ. For proof of this complete the activity given below.
Activity:
L.H.S. = `square`
= `square (1 - (sin^2θ)/(tan^2θ))`
= `tan^2θ (1 - square/((sin^2θ)/(cos^2θ)))`
= `tan^2θ (1 - (sin^2θ)/1 xx (cos^2θ)/square)`
= `tan^2θ (1 - square)`
= `tan^2θ xx square` ...[1 – cos2θ = sin2θ]
= R.H.S.
