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.
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
`(i) cos4^4 A – cos^2 A = sin^4 A – sin^2 A`
`(ii) cot^4 A – 1 = cosec^4 A – 2cosec^2 A`
`(iii) sin^6 A + cos^6 A = 1 – 3sin^2 A cos^2 A.`
If` (sec theta + tan theta)= m and ( sec theta - tan theta ) = n ,` show that mn =1
From the figure find the value of sinθ.
(cosec θ − sin θ) (sec θ − cos θ) (tan θ + cot θ) is equal to
If x = a cos θ and y = b sin θ, then b2x2 + a2y2 =
Prove the following identity :
`(cosecA - sinA)(secA - cosA)(tanA + cotA) = 1`
If sinA + cosA = m and secA + cosecA = n , prove that n(m2 - 1) = 2m
If cosθ + sinθ = `sqrt2` cosθ, show that cosθ - sinθ = `sqrt2` sinθ.
Choose the correct alternative:
tan (90 – θ) = ?
If 5 tan β = 4, then `(5 sin β - 2 cos β)/(5 sin β + 2 cos β)` = ______.
