Advertisements
Advertisements
प्रश्न
Prove the following identities:
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
Advertisements
उत्तर
L.H.S. `=(cosec A)/(cosecA - 1) + (cosecA)/(cosecA + 1)`
= `(cosec A (cosec A + 1) + cosec A (cosec A - 1))/((cosec A - 1) (cosec A + 1))`
= `(cosec^2 A+cosec A + cosec^2 A-cosec A)/((cosec A)^2 - (1)^2)`
= `(2 cosec^2 A)/(cosec^2 A - 1)`
= `(2 cosec^2 A)/(cot^2 A)` ...(∵ cosec2 A – 1 = cot2 A)
= `2(1/cancel(sin^2A))/(cos^2A/cancel(sin^2A))`
= `2/cos^2A`
= 2 sec2 A
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(1 + cos A)/sin^2 A = 1/(1 - cos A)`
if `a cos^3 theta + 3a cos theta sin^2 theta = m, a sin^3 theta + 3 a cos^2 theta sin theta = n`Prove that `(m + n)^(2/3) + (m - n)^(2/3)`
Prove the following identity :
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
Prove the following identities:
`(tan"A"+tan"B")/(cot"A"+cot"B")=tan"A"tan"B"`
Prove the following identity :
`(cosecθ)/(tanθ + cotθ) = cosθ`
A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/min.
If `cos theta/(1 + sin theta) = 1/"a"`, then prove that `("a"^2 - 1)/("a"^2 + 1)` = sin θ
Which is not correct formula?
Show that tan 7° × tan 23° × tan 60° × tan 67° × tan 83° = `sqrt(3)`.
Prove the following:
`1 + (cot^2 alpha)/(1 + "cosec" alpha)` = cosec α
