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प्रश्न
Prove the following identity :
`sqrt((1 + cosA)/(1 - cosA)) = cosecA + cotA`
उत्तर
= `sqrt((1 + cosA)/(1 - cosA) . (1 + cosA)/(1 + cosA))`
= `sqrt((1 + cosA)^2/(1 - cos^2A)) = sqrt((1 + cosA)^2/sin^2A)`
= `sqrt((1 + cos^2A)/sinA) = sqrt(1/sinA + cos^2A/sinA)`
= `sqrt((cosecA + cot^2A)`
= cosecA + cotA
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संबंधित प्रश्न
Prove the following trigonometric identities.
`(1 - cos theta)/sin theta = sin theta/(1 + cos theta)`
Prove that:
`(sinA - cosA)(1 + tanA + cotA) = secA/(cosec^2A) - (cosecA)/(sec^2A)`
`(sec^2 theta-1) cot ^2 theta=1`
`(sec^2 theta -1)(cosec^2 theta - 1)=1`
`sqrt((1+cos theta)/(1-cos theta)) + sqrt((1-cos theta )/(1+ cos theta )) = 2 cosec theta`
`(cot^2 theta ( sec theta - 1))/((1+ sin theta))+ (sec^2 theta(sin theta-1))/((1+ sec theta))=0`
Write True' or False' and justify your answer the following :
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Prove that (sin θ + cosec θ)2 + (cos θ + sec θ)2 = 7 + tan2 θ + cot2 θ.
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