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प्रश्न
Prove that : `1 - (cos^2 θ)/(1 + sin θ) = sin θ`.
उत्तर
LHS = `1 - (cos^2 θ)/(1 + sin θ)`
= `1 - (1 - sin^2 θ)/(1 + sin θ)`
= `1 - ((1 - sin θ)(1 + sin θ))/(1 + sin θ)`
= 1 - ( 1 - sin θ )
= 1 - 1 + sin θ
= sin θ
= RHS
Hence proved.
APPEARS IN
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Activity:
L.H.S = `square`
= `square (1 - (sin^2theta)/(tan^2theta))`
= `tan^2theta (1 - square/((sin^2theta)/(cos^2theta)))`
= `tan^2theta (1 - (sin^2theta)/1 xx (cos^2theta)/square)`
= `tan^2theta (1 - square)`
= `tan^2theta xx square` .....[1 – cos2θ = sin2θ]
= R.H.S
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