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प्रश्न
Prove that `sqrt((1 + cos A)/(1 - cos A)) = (tan A + sin A)/(tan A. sin A)`
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उत्तर
LHS = `sqrt(((1 + cos A)(1 + cos A))/((1 - cos A)(1 + cos A)))`
= `sqrt((1 + cos A)^2/(1 - cos^2 A))`
= `sqrt((1 + cos^2 A + 2cos A)/sin^2 A`
= `(1 + cos A)/sin A`
RHS = `(tan A + sin A)/(tan A sin A)`
= `(sin A(1/cos A + 1))/((sin A/cos A xx sin A)`
= `(sin A( 1 + cos A))/cos A xx cos A/(sin A sin A)`
= `(1 + cos A)/sin A`
Hence proved.
संबंधित प्रश्न
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Prove the following identity :
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
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.
Prove that `(cot A)/(1 - cot A) + (tan A)/(1 - tan A) = -1`.
