Advertisements
Advertisements
Question
If `cosA/cosB = m` and `cosA/sinB = n`, show that : (m2 + n2) cos2 B = n2.
Advertisements
Solution
L.H.S. = (m2 + n2) cos2 B
= `(cos^2A/cos^2B + cos^2A/sin^2B)cos^2B`
= `((cos^2Asin^2B + cos^2Acos^2B)/(cos^2Bsin^2B))cos^2B`
= `((cos^2Asin^2B + cos^2Acos^2B)/sin^2B)`
= `(cos^2A(sin^2B + cos^2B))/sin^2B`
= `cos^2A/sin^2B`
= n2
Hence, (m2 + n2) cos2 B = n2.
APPEARS IN
RELATED QUESTIONS
Prove that sin6θ + cos6θ = 1 – 3 sin2θ. cos2θ.
If m=(acosθ + bsinθ) and n=(asinθ – bcosθ) prove that m2+n2=a2+b2
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 the following identities:
(1 + cot A – cosec A)(1 + tan A + sec A) = 2
Prove that:
`(sin^2θ)/(cosθ) + cosθ = secθ`
Prove the following identity :
`(secA - 1)/(secA + 1) = (1 - cosA)/(1 + cosA)`
Prove the following identity :
`cos^4A - sin^4A = 2cos^2A - 1`
Prove the following identity :
`cosA/(1 - tanA) + sinA/(1 - cotA) = sinA + cosA`
Prove the following identity :
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
If `sin θ + cos θ = sqrt(3)`, then show that tan θ + cot θ = 1.
