Advertisements
Advertisements
प्रश्न
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
उत्तर
L.H.S. = `cosA/(1-sinA)`
= `(cosA(1 + sinA))/((1 - sinA)(1 + sinA))`
= `(cosA(1 + sinA))/(1 - sin^2A)`
= `(cosA(1 + sinA))/(cos^2A)`
= `(1 + sinA)/cosA`
= `1/cosA + sinA/cosA`
= sec A + tan A = R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove that `cosA/(1+sinA) + tan A = secA`
Prove that `(tan^2 theta)/(sec theta - 1)^2 = (1 + cos theta)/(1 - cos theta)`
Prove the following trigonometric identities.
`sqrt((1 - cos theta)/(1 + cos theta)) = cosec theta - cot theta`
Prove the following identities:
cot2 A – cos2 A = cos2 A . cot2 A
Prove the following identities:
`1/(sinA + cosA) + 1/(sinA - cosA) = (2sinA)/(1 - 2cos^2A)`
`tan theta /((1 - cot theta )) + cot theta /((1 - tan theta)) = (1+ sec theta cosec theta)`
Define an identity.
Prove that `tan^3 θ/( 1 + tan^2 θ) + cot^3 θ/(1 + cot^2 θ) = sec θ. cosec θ - 2 sin θ cos θ.`
If sin θ (1 + sin2 θ) = cos2 θ, then prove that cos6 θ – 4 cos4 θ + 8 cos2 θ = 4
Choose the correct alternative:
cos θ. sec θ = ?
