Advertisements
Advertisements
प्रश्न
Prove the following identity :
`sec^2A.cosec^2A = tan^2A + cot^2A + 2`
Advertisements
उत्तर
LHS = `sec^2A.cosec^2A = 1/(cos^2A.sin^2A)`
RHS = `tan^2A + cot^2A + 2 = tan^2A + cot^2A + 2tan^2A.cot^2A`
= `(tanA + cotA)^2 = (sinA/cosA + cosA/sinA)^2`
= `((sin^2A + cos^2A)/(sinA.cosA))^2 = 1/(cos^2A.sin^2A)`
= Hence , LHS = RHS
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
(cosec θ − sec θ) (cot θ − tan θ) = (cosec θ + sec θ) ( sec θ cosec θ − 2)
Prove the following identities:
`1/(tan A + cot A) = cos A sin A`
Prove the following identities:
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
`(tan A + tanB )/(cot A + cot B) = tan A tan B`
Prove the following identity :
`(1 + cosA)/(1 - cosA) = (cosecA + cotA)^2`
Prove that:
`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = 2cosectheta`
Prove that `sqrt(2 + tan^2 θ + cot^2 θ) = tan θ + cot θ`.
Prove the following identities.
sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
Prove that `(cot A + "cosec" A - 1)/(cot A - "cosec" A + 1) = (1 + cos A)/(sin A)`.
If 2sin2θ – cos2θ = 2, then find the value of θ.
