Advertisements
Advertisements
प्रश्न
Prove the following identity :
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
उत्तर
LHS = `(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA)`
= `((sinA + cosA)^2 + (sinA - cosA)^2)/((sinA + cosA)(sinA - cosA))`
= `(sin^2A + cos^2A + 2sinA cosA + sin^2A + cos^2A - 2sinA cosA)/(sin^2A - cos^2A)`
= `(2(sin^2A + cos^2A))/(sin^2A - cos^2A)`
= `2/(sin^2A - cos^2A)` [`sin^2A + cos^2A = 1`]
= `2/(sin^2A - cos^2A) = 2/(sin^2A - (1 - sin^2A))`
⇒ `2/(2sin^2A - 1)`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(cos^2 theta)/sin theta - cosec theta + sin theta = 0`
Prove the following identities:
`cot^2A((secA - 1)/(1 + sinA)) + sec^2A((sinA - 1)/(1 + secA)) = 0`
Eliminate θ, if
x = 3 cosec θ + 4 cot θ
y = 4 cosec θ – 3 cot θ
What is the value of (1 + tan2 θ) (1 − sin θ) (1 + sin θ)?
Prove the following identity :
tanA+cotA=secAcosecA
Prove the following identity :
secA(1 + sinA)(secA - tanA) = 1
Prove the following identity :
`cos^4A - sin^4A = 2cos^2A - 1`
Prove that cot θ. tan (90° - θ) - sec (90° - θ). cosec θ + 1 = 0.
Simplify (1 + tan2θ)(1 – sinθ)(1 + sinθ)
If tan θ = `x/y`, then cos θ is equal to ______.
