Advertisements
Advertisements
Question
Prove the following identities:
(1 + cot A – cosec A)(1 + tan A + sec A) = 2
Advertisements
Solution
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
RELATED QUESTIONS
9 sec2 A − 9 tan2 A = ______.
Prove the following identities:
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = sec A + tan A`
Prove that:
`(tanA + 1/cosA)^2 + (tanA - 1/cosA)^2 = 2((1 + sin^2A)/(1 - sin^2A))`
Prove the following identity :
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
Prove the following identity :
`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`
Prove that: sin6θ + cos6θ = 1 - 3sin2θ cos2θ.
Prove the following identities.
sec6 θ = tan6 θ + 3 tan2 θ sec2 θ + 1
If 3 sin θ = 4 cos θ, then sec θ = ?
Prove that `(tan(90 - θ) + cot(90 - θ))/("cosec" θ) = sec θ`.
