Advertisements
Advertisements
प्रश्न
Prove the following identities:
`(1 - cosA)/sinA + sinA/(1 - cosA)= 2cosecA`
Advertisements
उत्तर
`(1 - cosA)/sinA + sinA/(1 - cosA)`
= `((1 - cosA)^2 + sin^2A)/(sinA(1 - cosA))`
= `(1 + cos^2A - 2cosA + sin^2A)/(sinA(1 - cosA))`
= `(2 - 2cosA)/(sinA(1 - cosA))`
= `(2(1 - cosA))/(sinA(1 - cosA))`
= 2 cosec A
संबंधित प्रश्न
Prove the following trigonometric identities.
`sqrt((1 - cos theta)/(1 + cos theta)) = cosec theta - cot theta`
Prove the following trigonometric identities.
`(cot A + tan B)/(cot B + tan A) = cot A tan B`
Prove that:
`tanA/(1 - cotA) + cotA/(1 - tanA) = secA "cosec" A + 1`
If cosec θ − cot θ = α, write the value of cosec θ + cot α.
Write True' or False' and justify your answer the following :
The value of \[\sin \theta\] is \[x + \frac{1}{x}\] where 'x' is a positive real number .
If a cos θ + b sin θ = m and a sin θ − b cos θ = n, then a2 + b2 =
Prove the following identity :
`(secA - 1)/(secA + 1) = (1 - cosA)/(1 + cosA)`
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
Prove that `sin^2 θ/ cos^2 θ + cos^2 θ/sin^2 θ = 1/(sin^2 θ. cos^2 θ) - 2`.
Prove that: sin6θ + cos6θ = 1 - 3sin2θ cos2θ.
