Advertisements
Advertisements
प्रश्न
Prove the following identities:
(1 + cot A – cosec A)(1 + tan A + sec A) = 2
Advertisements
उत्तर
L.H.S. = (1 + cot A – cosec A)(1 + tan A + sec A)
= `(1 + cosA/sinA - 1/sinA)(1 + sinA/cosA + 1/cosA)`
= `((sinA + cosA - 1)/sinA)((cosA + sinA + 1)/cosA)`
= `((sinA + cosA - 1)(sinA + cosA + 1))/(sinAcosA)`
= `((sinA + cosA)^2 - (1)^2)/(sinAcosA)`
= `(sin^2A + cos^2A + 2sinAcosA - 1)/(sinAcosA)`
= `(1 + 2sinAcosA - 1)/(sinAcosA)`
= `(2sinAcosA)/(sinAcosA)`
= 2 = R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`tan A/(1 + tan^2 A)^2 + cot A/((1 + cot^2 A)) = sin A cos A`
Prove the following identities:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
Prove the following identities:
(cosec A + sin A) (cosec A – sin A) = cot2 A + cos2 A
Prove the following identity :
`tan^2A - tan^2B = (sin^2A - sin^2B)/(cos^2Acos^2B)`
Prove the following identity :
`tan^2θ/(tan^2θ - 1) + (cosec^2θ)/(sec^2θ - cosec^2θ) = 1/(sin^2θ - cos^2θ)`
Find the value of sin 30° + cos 60°.
Prove that:
`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = 2cosectheta`
Prove the following identities:
`(1 - tan^2 θ)/(cot^2 θ - 1) = tan^2 θ`.
If x = a tan θ and y = b sec θ then
If cos 9α = sinα and 9α < 90°, then the value of tan5α is ______.
