Advertisements
Advertisements
प्रश्न
Prove that:
(cosec A – sin A) (sec A – cos A) sec2 A = tan A
Advertisements
उत्तर
L.H.S. = (cosec A – sin A) (sec A – cos A) × sec2 A
= `(1/sinA - sinA)(1/cosA - cosA) xx sec^2A` ...`{∵ cosec theta = 1/sintheta, sectheta = 1/costheta, 1 - sin^2theta = cos^2theta, 1 - cos^2theta = sin^2theta}`
= `((1 - sin^2A)/sinA)((1 - cos^2A)/cosA) 1/(cos^2A)`
= `(cos^2A)/(sinA)*(sin^2A)/(cosA)*1/(cos^2A)`
= `sinA/cosA`
= tan A = R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`1 + cot^2 theta/(1 + cosec theta) = cosec theta`
Given that:
(1 + cos α) (1 + cos β) (1 + cos γ) = (1 − cos α) (1 − cos α) (1 − cos β) (1 − cos γ)
Show that one of the values of each member of this equality is sin α sin β sin γ
Prove the following identities:
`(secA - tanA)/(secA + tanA) = 1 - 2secAtanA + 2tan^2A`
`(1-cos^2theta) sec^2 theta = tan^2 theta`
`sec theta (1- sin theta )( sec theta + tan theta )=1`
Prove the following identity :
`(secA - 1)/(secA + 1) = (1 - cosA)/(1 + cosA)`
If tanA + sinA = m and tanA - sinA = n , prove that (`m^2 - n^2)^2` = 16mn
Prove that:
`(cos^3 θ + sin^3 θ)/(cos θ + sin θ) + (cos^3 θ - sin^3 θ)/(cos θ - sin θ) = 2`
Prove that `"cosec" θ xx sqrt(1 - cos^2θ) = 1`.
Let x1, x2, x3 be the solutions of `tan^-1((2x + 1)/(x + 1)) + tan^-1((2x - 1)/(x - 1))` = 2tan–1(x + 1) where x1 < x2 < x3 then 2x1 + x2 + x32 is equal to ______.
