Advertisements
Advertisements
Question
Prove that:
`1/(cosA + sinA - 1) + 1/(cosA + sinA + 1) = cosecA + secA`
Solution
L.H.S. = `1/(cosA + sinA - 1) + 1/(cosA + sinA + 1)`
= `(cosA + sinA + 1 + cosA + sinA - 1)/((cosA + sinA)^2 - 1)`
= `(2(cosA + sinA))/(cos^2A + sin^2A + 2cosAsinA - 1)`
= `(2(cosA + sinA))/(1 + 2cosAsinA - 1)`
= `(cosA + sinA)/(cosAsinA)`
= `cosA/(cosAsinA) + sinA/(cosAsinA)`
= `1/sinA + 1/cosA`
= cosec A + sec A = R.H.S.
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities
(1 + cot2 A) sin2 A = 1
Prove the following trigonometric identities
`cos theta/(1 - sin theta) = (1 + sin theta)/cos theta`
Prove the following trigonometric identities.
`(cos theta)/(cosec theta + 1) + (cos theta)/(cosec theta - 1) = 2 tan theta`
Prove the following trigonometric identities.
(cosec θ − sec θ) (cot θ − tan θ) = (cosec θ + sec θ) ( sec θ cosec θ − 2)
Prove the following trigonometric identities.
`cot^2 A cosec^2B - cot^2 B cosec^2 A = cot^2 A - cot^2 B`
Prove the following identities:
`(sinAtanA)/(1 - cosA) = 1 + secA`
The value of sin2 29° + sin2 61° is
Prove that (cosec A - sin A)( sec A - cos A) sec2 A = tan A.
Prove that `(sintheta + tantheta)/cos theta` = tan θ(1 + sec θ)
Prove that cosec θ – cot θ = `sin theta/(1 + cos theta)`
