Advertisements
Advertisements
Question
Prove the following identity :
`(1 - cos^2θ)sec^2θ = tan^2θ`
Advertisements
Solution
`(1 - cos^2θ)sec^2θ = tan^2θ`
Consider L.H.S = `sin^2θ1/cos^2θ`
= `tan^2θ` = RHS
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities
`(1 + tan^2 theta)/(1 + cot^2 theta) = ((1 - tan theta)/(1 - cot theta))^2 = tan^2 theta`
Prove the following trigonometric identities.
`1/(sec A + tan A) - 1/cos A = 1/cos A - 1/(sec A - tan A)`
Prove the following trigonometric identities.
(sec A − cosec A) (1 + tan A + cot A) = tan A sec A − cot A cosec A
Prove the following identities:
(sec A – cos A) (sec A + cos A) = sin2 A + tan2 A
Prove the following identities:
sec2 A . cosec2 A = tan2 A + cot2 A + 2
Prove the following identities:
`(1 - cosA)/sinA + sinA/(1 - cosA)= 2cosecA`
Find the value of sin ` 48° sec 42° + cos 48° cosec 42°`
If `sin theta = x , " write the value of cot "theta .`
Prove the following identity :
`1/(tanA + cotA) = sinAcosA`
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)) + sqrt((1 - sin theta)/(1 + sin theta))` = 2 sec θ
