Advertisements
Advertisements
प्रश्न
If sin A + cos A = m and sec A + cosec A = n, show that : n (m2 – 1) = 2 m
Advertisements
उत्तर
Given:
sin A + cos A = m and sec A + cosec A = n
Consider L.H.S = n (m2 – 1)
= `(secA + cosecA)[(sinA + cosA)^2 - 1]`
= `(1/cosA + 1/sinA)[sin^2A + cos^2A + 2sinAcosA - 1]`
= `((cosA + sinA)/(sinAcosA))(1 + 2sinAcosA - 1)`
= `((cosA + sinA))/(sinAcosA)(2sinAcosA)`
= 2(sin A + cos A)
= 2 m = R.H.S
APPEARS IN
संबंधित प्रश्न
If sinθ + cosθ = p and secθ + cosecθ = q, show that q(p2 – 1) = 2p
Prove the following trigonometric identities.
`[tan θ + 1/cos θ]^2 + [tan θ - 1/cos θ]^2 = 2((1 + sin^2 θ)/(1 - sin^2 θ))`
If a cos θ + b sin θ = m and a sin θ – b cos θ = n, prove that a2 + b2 = m2 + n2
`sin theta / ((1+costheta))+((1+costheta))/sin theta=2cosectheta`
Write True' or False' and justify your answer the following :
The value of the expression \[\sin {80}^° - \cos {80}^°\]
If sin θ + cos θ = a and sec θ + cosec θ = b , then the value of b(a2 – 1) is equal to
Prove that `(sin θ + "cosec" θ)/(sin θ) = 2 + cot^2θ`.
Prove that `sec^2A - "cosec"^2A = (2sin^2A - 1)/(sin^2A *cos^2A)`.
If cos A + cos2A = 1, then sin2A + sin4A = ?
Prove that (1 – cos2A) . sec2B + tan2B (1 – sin2A) = sin2A + tan2B.
