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प्रश्न
`(sin A)/(1 + cos A) + (1 + cos A)/(sin A)` = 2 cosec A
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उत्तर
LHS = `((sin^2 A + ( 1 + cos A)^2)/((1 + cos A)sin A))`
= `(sin^2 A + 1 + cos^2 A + 2 cos A)/((1 + cos A) sin A)`
= `(1 + 1 + 2 cos A)/((1 + cos A) sin A)`
= `(2(1 + cos A))/((1 + cos A)sin A)`
= 2 cosec A
= RHS
Hence proved.
संबंधित प्रश्न
If `x/a=y/b = z/c` show that `x^3/a^3 + y^3/b^3 + z^3/c^3 = (3xyz)/(abc)`.
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
`(1-cos^2theta) sec^2 theta = tan^2 theta`
`(tan^2theta)/((1+ tan^2 theta))+ cot^2 theta/((1+ cot^2 theta))=1`
`(sin theta +cos theta )/(sin theta - cos theta)+(sin theta- cos theta)/(sin theta + cos theta) = 2/((sin^2 theta - cos ^2 theta)) = 2/((2 sin^2 theta -1))`
If `sin theta = 1/2 , " write the value of" ( 3 cot^2 theta + 3).`
If `sec theta + tan theta = x," find the value of " sec theta`
Prove that:
`(cot A - 1)/(2 - sec^2 A) = cot A/(1 + tan A)`
If sec θ = `25/7`, find the value of tan θ.
Solution:
1 + tan2 θ = sec2 θ
∴ 1 + tan2 θ = `(25/7)^square`
∴ tan2 θ = `625/49 - square`
= `(625 - 49)/49`
= `square/49`
∴ tan θ = `square/7` ........(by taking square roots)
If tan θ = `x/y`, then cos θ is equal to ______.
