Advertisements
Advertisements
प्रश्न
Prove the following identities:
(cosec A – sin A) (sec A – cos A) (tan A + cot A) = 1
Prove that:
(cosec A − sin A) (sec A – cos A) (tan A + cot A) = 1
Advertisements
उत्तर
L.H.S. = (cosec A – sin A) (sec A – cos A) (tan A + cot A)
= `(1/sinA - sinA)(1/cosA - cosA)(1/tanA + tanA)`
= `((1 - sin^2A)/sinA)((1 - cos^2A)/cosA)(sinA/cosA + cosA/sinA)`
= `(cos^2A/sinA)(sin^2A/cosA)((sin^2A + cos^2A)/(sinA.cosA))`
= `(cos^2A/sinA)(sin^2A/cosA)((1)/(sinA.cosA))`
= `(cos^2A sin^2A)/((sinA .cosA)(sinA.cosA ))`
= `(cos^2A sin^2A)/(sin^2A cos^2A)`
= 1
= R.H.S.
संबंधित प्रश्न
Prove that:
`tanA/(1 - cotA) + cotA/(1 - tanA) = secA "cosec" A + 1`
`tan theta/(1+ tan^2 theta)^2 + cottheta/(1+ cot^2 theta)^2 = sin theta cos theta`
If (tan θ + sin θ) = m and (tan θ – sin θ) = n, prove that (m2 – n2)2 = 16 mn.
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
Prove that `sin(90^circ - A).cos(90^circ - A) = tanA/(1 + tan^2A)`
`(sin A)/(1 + cos A) + (1 + cos A)/(sin A)` = 2 cosec A
If tan A + sin A = m and tan A − sin A = n, then show that `m^2 - n^2 = 4 sqrt (mn)`.
Prove that `tan^3 θ/( 1 + tan^2 θ) + cot^3 θ/(1 + cot^2 θ) = sec θ. cosec θ - 2 sin θ cos θ.`
Prove that: `1/(cosec"A" - cot"A") - 1/sin"A" = 1/sin"A" - 1/(cosec"A" + cot"A")`
If cosec θ + cot θ = p, then prove that cos θ = `(p^2 - 1)/(p^2 + 1)`
