Advertisements
Advertisements
Question
If sin A + cos A = p and sec A + cosec A = q, then prove that : q(p2 – 1) = 2p.
Advertisements
Solution
q(p2 – 1) = (sec A + cosec A) [(sin A + cos A)2 – 1]
= (sec A + cosec A) [(sin2 A + cos2 A + 2 sin A cos A) – 1]
= (sec A + cosec A) [(1 + 2 sin A cos A) – 1]
= (sec A + cosec A) (2 sin A cos A)
= 2 sin A + 2 cos A
= 2p
RELATED QUESTIONS
Prove the following trigonometric identities.
`((1 + tan^2 theta)cot theta)/(cosec^2 theta) = tan theta`
Prove the following trigonometric identities.
`(tan A + tan B)/(cot A + cot B) = tan A tan B`
Prove the following identities:
`cosecA - cotA = sinA/(1 + cosA)`
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
Prove the following identities:
`(1 + (secA - tanA)^2)/(cosecA(secA - tanA)) = 2tanA`
Prove that:
`cot^2A/(cosecA - 1) - 1 = cosecA`
Express (sin 67° + cos 75°) in terms of trigonometric ratios of the angle between 0° and 45°.
Prove that sec θ. cosec (90° - θ) - tan θ. cot( 90° - θ ) = 1.
Prove the following identities: sec2 θ + cosec2 θ = sec2 θ cosec2 θ.
If tan θ = `13/12`, then cot θ = ?
