Advertisements
Advertisements
Question
Prove the following identity :
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
Advertisements
Solution
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
LHS = `(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1)`
= `(cosec^2A + cosecA + cosec^2A - cosecA)/(cosec^2A - 1)`
= `(2cosec^2A)/cot^2A(Q cosec^2A - 1 = cot^2A)`
= `(2/sin^2A)/(cos^2A/sin^2A) = 2/cos^2A = 2sec^2A`
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
tan2 A sec2 B − sec2 A tan2 B = tan2 A − tan2 B
Prove the following identities:
`cosecA + cotA = 1/(cosecA - cotA)`
Prove the following identities:
`1 - sin^2A/(1 + cosA) = cosA`
Prove the following identities:
`(sec theta + tan theta)/(sec theta - tan theta) = (sec theta + tan theta)^2 = 1 + 2 tan^2 theta + 2 sec theta tan theta`
If`( 2 sin theta + 3 cos theta) =2 , " prove that " (3 sin theta - 2 cos theta) = +- 3.`
If `sec theta + tan theta = p,` prove that
(i)`sec theta = 1/2 ( p+1/p) (ii) tan theta = 1/2 ( p- 1/p) (iii) sin theta = (p^2 -1)/(p^2+1)`
If `sec theta = x ,"write the value of tan" theta`.
If cos \[9\theta\] = sin \[\theta\] and \[9\theta\] < 900 , then the value of tan \[6 \theta\] is
If `x/(a cosθ) = y/(b sinθ) "and" (ax)/cosθ - (by)/sinθ = a^2 - b^2 , "prove that" x^2/a^2 + y^2/b^2 = 1`
Prove that `sec^2A - "cosec"^2A = (2sin^2A - 1)/(sin^2A *cos^2A)`.
