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प्रश्न
Prove the following identities:
`(1+ sin A)/(cosec A - cot A) - (1 - sin A)/(cosec A + cot A) = 2(1 + cot A)`
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उत्तर
L.H.S. = `(1 + sin A)/(cosec A - cot A) - (1 - sin A)/(cosec A + cot A)`
= `((1 + sin A)(cosec A + cot A) - (1 - sin A)(cosec A - cot A))/((cosec A - cot A)(cosec A + cot A))`
= `(cosec A + cot A + sin A cosec A + sin A cot A - cosec A + cot A + sin A cosec A - sin A cos A)/(cosec^2A - cot^2A)`
= 2 cot A + 2 sin A cosec A
= 2 cot A + 2 `1/(cosec A) xx cosec A`
= 2 (cot A + 1)
Hence proved.
संबंधित प्रश्न
Prove that ` \frac{\sin \theta -\cos \theta +1}{\sin\theta +\cos \theta -1}=\frac{1}{\sec \theta -\tan \theta }` using the identity sec2 θ = 1 + tan2 θ.
Prove the following trigonometric identities.
(1 + cot A − cosec A) (1 + tan A + sec A) = 2
Prove that:
`1/(sinA - cosA) - 1/(sinA + cosA) = (2cosA)/(2sin^2A - 1)`
`(1+ tan^2 theta)/(1+ tan^2 theta)= (cos^2 theta - sin^2 theta)`
`sqrt((1+cos theta)/(1-cos theta)) + sqrt((1-cos theta )/(1+ cos theta )) = 2 cosec theta`
Write True' or False' and justify your answer the following :
The value of sin θ+cos θ is always greater than 1 .
Prove the following identity :
`(cotA + tanB)/(cotB + tanA) = cotAtanB`
Prove the following identity :
`cosecA + cotA = 1/(cosecA - cotA)`
Choose the correct alternative:
tan (90 – θ) = ?
(1 + sin A)(1 – sin A) is equal to ______.
