Advertisements
Advertisements
प्रश्न
Prove the following identity :
`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))` = 2secq
Advertisements
उत्तर
`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))`
= `sqrt((1 + sinq)/(1 - sinq) . (1+ sinq)/(1 + sinq)) + sqrt((1 - sinq)/(1 + sinq) . (1 - sinq)/(1 - sinq))`
= `sqrt((1 + sinq)^2/(1 - sin^2q)` + `sqrt((1 - sinq)^2/(1 - sin^2q))` = `sqrt((1 + sinq)^2/cos^2q)` + `sqrt((1 - sinq)^2/cos^2q)`
= `(1 + sinq)/cosq + (1 - sinq)/cosq = (1 + sinq + 1 - sinq)/cosq` = `2/cosq`
= 2 secq
APPEARS IN
संबंधित प्रश्न
Evaluate
`(sin ^2 63^@ + sin^2 27^@)/(cos^2 17^@+cos^2 73^@)`
Prove the following trigonometric identities.
`tan theta + 1/tan theta` = sec θ.cosec θ
Prove the following trigonometric identities.
`(tan^3 theta)/(1 + tan^2 theta) + (cot^3 theta)/(1 + cot^2 theta) = sec theta cosec theta - 2 sin theta cos theta`
Prove that:
2 sin2 A + cos4 A = 1 + sin4 A
`(sin theta)/((sec theta + tan theta -1)) + cos theta/((cosec theta + cot theta -1))=1`
`(tan A + tanB )/(cot A + cot B) = tan A tan B`
Write the value of `cosec^2 theta (1+ cos theta ) (1- cos theta).`
Prove that: 2(sin6θ + cos6θ) - 3 ( sin4θ + cos4θ) + 1 = 0.
Prove that cosec θ – cot θ = `(sin θ)/(1 + cos θ)`.
If tan θ = 3, then `(4 sin theta - cos theta)/(4 sin theta + cos theta)` is equal to ______.
