Advertisements
Advertisements
प्रश्न
Prove the following trigonometric identities.
`cot^2 A cosec^2B - cot^2 B cosec^2 A = cot^2 A - cot^2 B`
Advertisements
उत्तर
L.H.S = `cot^2 A cosec^2B - cot^2 B cosec^2 A`
`= cot^2 A(1+ cot^2 B) - cot^2 B(1 + cot^2 A)` (∵ `1 + cot^2 theta = cosec^2 theta`)
`= cot^2 A + cot^2 A cot^2 B - cot^2 B cot^2 A`
`= cot^2 A - cot^2 B`
Hence proved
APPEARS IN
संबंधित प्रश्न
If m=(acosθ + bsinθ) and n=(asinθ – bcosθ) prove that m2+n2=a2+b2
Prove the following trigonometric identities.
(1 + tan2θ) (1 − sinθ) (1 + sinθ) = 1
`Prove the following trigonometric identities.
`(sec A - tan A)^2 = (1 - sin A)/(1 + sin A)`
Prove the following trigonometric identities.
(sec A − cosec A) (1 + tan A + cot A) = tan A sec A − cot A cosec A
If a cos θ + b sin θ = m and a sin θ – b cos θ = n, prove that a2 + b2 = m2 + n2
Prove the following identities:
`sqrt((1 - sinA)/(1 + sinA)) = cosA/(1 + sinA)`
If x cos A + y sin A = m and x sin A – y cos A = n, then prove that : x2 + y2 = m2 + n2
If 4 cos2 A – 3 = 0, show that: cos 3 A = 4 cos3 A – 3 cos A
Prove that:
(tan A + cot A) (cosec A – sin A) (sec A – cos A) = 1
`cosec theta (1+costheta)(cosectheta - cot theta )=1`
`sin^2 theta + cos^4 theta = cos^2 theta + sin^4 theta`
Show that none of the following is an identity:
`tan^2 theta + sin theta = cos^2 theta`
If sin2 θ cos2 θ (1 + tan2 θ) (1 + cot2 θ) = λ, then find the value of λ.
Prove the following identity :
`sec^2A + cosec^2A = sec^2Acosec^2A`
Find A if tan 2A = cot (A-24°).
Prove that: `(sin θ - 2sin^3 θ)/(2 cos^3 θ - cos θ) = tan θ`.
Choose the correct alternative:
sec2θ – tan2θ =?
Prove that
`(cot "A" + "cosec A" - 1)/(cot"A" - "cosec A" + 1) = (1 + cos "A")/"sin A"`
If 1 + sin2θ = 3 sin θ cos θ, then prove that tan θ = 1 or `1/2`.
`1/sin^2θ - 1/cos^2θ - 1/tan^2θ - 1/cot^2θ - 1/sec^2θ - 1/("cosec"^2θ) = -3`, then find the value of θ.
