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
Prove the identity (sin θ + cos θ)(tan θ + cot θ) = sec θ + cosec θ.
Prove the following trigonometric identities.
`(1/(sec^2 theta - cos theta) + 1/(cosec^2 theta - sin^2 theta)) sin^2 theta cos^2 theta = (1 - sin^2 theta cos^2 theta)/(2 + sin^2 theta + cos^2 theta)`
Given that:
(1 + cos α) (1 + cos β) (1 + cos γ) = (1 − cos α) (1 − cos α) (1 − cos β) (1 − cos γ)
Show that one of the values of each member of this equality is sin α sin β sin γ
Prove the following identities:
`(1 - sinA)/(1 + sinA) = (secA - tanA)^2`
Prove the following identities:
`(1+ sin A)/(cosec A - cot A) - (1 - sin A)/(cosec A + cot A) = 2(1 + cot A)`
Prove that:
`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`
`(1-tan^2 theta)/(cot^2-1) = tan^2 theta`
` (sin theta + cos theta )/(sin theta - cos theta ) + ( sin theta - cos theta )/( sin theta + cos theta) = 2/ ((1- 2 cos^2 theta))`
If sec2 θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.
Prove the following identity :
tanA+cotA=secAcosecA
Prove the following identity :
`sqrt((secq - 1)/(secq + 1)) + sqrt((secq + 1)/(secq - 1))` = 2 cosesq
If tan θ = 2, where θ is an acute angle, find the value of cos θ.
If sin θ = `1/2`, then find the value of θ.
Prove that (cosec A - sin A)( sec A - cos A) sec2 A = tan A.
Prove that:
`(sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = 2/(2 sin^2 A - 1)`
Prove that `sin^2 θ/ cos^2 θ + cos^2 θ/sin^2 θ = 1/(sin^2 θ. cos^2 θ) - 2`.
Prove that `(sin 70°)/(cos 20°) + (cosec 20°)/(sec 70°) - 2 cos 70° xx cosec 20°` = 0.
If A + B = 90°, show that sec2 A + sec2 B = sec2 A. sec2 B.
If `1 - cos^2θ = 1/4`, then θ = ?
If sinA + sin2A = 1, then the value of the expression (cos2A + cos4A) is ______.
