Advertisements
Advertisements
प्रश्न
Prove the following trigonometric identities.
`(cot A + tan B)/(cot B + tan A) = cot A tan B`
Advertisements
उत्तर
We have to prove `(cot A + tan B)/(cot B + tan A) = cot A tan B`
Now
`(cot A + tan B)/(cot B + tan A) = (cot A + 1/cot B)/(cot B + 1/cot A)`
`= ((cot A cot B + 1)/cot B)/((cot A cot B +1)/cot A)`
`= cot A/cot B`
`= cot A 1/cot B`
= cot A tan B
Hence proved
APPEARS IN
संबंधित प्रश्न
If `sec alpha=2/sqrt3` , then find the value of `(1-cosecalpha)/(1+cosecalpha)` where α is in IV quadrant.
Prove the following identities:
`(i) 2 (sin^6 θ + cos^6 θ) –3(sin^4 θ + cos^4 θ) + 1 = 0`
`(ii) (sin^8 θ – cos^8 θ) = (sin^2 θ – cos^2 θ) (1 – 2sin^2 θ cos^2 θ)`
Prove that `cosA/(1+sinA) + tan A = secA`
Prove that `(sin theta)/(1-cottheta) + (cos theta)/(1 - tan theta) = cos theta + sin theta`
Prove the following trigonometric identities
(1 + cot2 A) sin2 A = 1
Prove the following trigonometric identities. `(1 - cos A)/(1 + cos A) = (cot A - cosec A)^2`
Prove the following trigonometric identities.
`1/(sec A - 1) + 1/(sec A + 1) = 2 cosec A cot 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:
`cot^2A/(cosecA + 1)^2 = (1 - sinA)/(1 + sinA)`
Prove the following identities:
`cosA/(1 + sinA) + tanA = secA`
Prove the following identities:
cosec4 A (1 – cos4 A) – 2 cot2 A = 1
`sqrt((1-cos theta)/(1+cos theta)) = (cosec theta - cot theta)`
`(sin theta+1-cos theta)/(cos theta-1+sin theta) = (1+ sin theta)/(cos theta)`
If sec θ + tan θ = x, then sec θ =
Prove the following identity :
`(secA - 1)/(secA + 1) = (1 - cosA)/(1 + cosA)`
Prove the following identity :
`1/(sinA + cosA) + 1/(sinA - cosA) = (2sinA)/(1 - 2cos^2A)`
If cosθ = `5/13`, then find sinθ.
If sec θ + tan θ = m, show that `(m^2 - 1)/(m^2 + 1) = sin theta`
Prove that `sqrt((1 + sin θ)/(1 - sin θ))` = sec θ + tan θ.
Prove that `(1 + sec A)/(sec A) = (sin^2A)/(1 - cos A)`.
