Advertisements
Advertisements
प्रश्न
Prove the following trigonometric identities.
`sin^2 A + 1/(1 + tan^2 A) = 1`
Advertisements
उत्तर
We know that,
`sin^2 A + cos^2 A = 1`
`sec^2 A - tan^2A = 1`
So
`sin^2 A + 1/(1 + tan^2 A) = sin^2 A + 1/sec^2 A`
`= sin^2 A + (1/sec A)^2`
`= sin^2 A + (cos A)^2`
`= sin^2 A + cos^2 A`
= 1
APPEARS IN
संबंधित प्रश्न
Prove that: `(1 – sinθ + cosθ)^2 = 2(1 + cosθ)(1 – sinθ)`
Prove the following trigonometric identities
cosec6θ = cot6θ + 3 cot2θ cosec2θ + 1
if `x/a cos theta + y/b sin theta = 1` and `x/a sin theta - y/b cos theta = 1` prove that `x^2/a^2 + y^2/b^2 = 2`
Prove the following identities:
cosec A(1 + cos A) (cosec A – cot A) = 1
Prove the following identities:
`(cosecA - 1)/(cosecA + 1) = (cosA/(1 + sinA))^2`
Prove the following identities:
`cot^2A((secA - 1)/(1 + sinA)) + sec^2A((sinA - 1)/(1 + secA)) = 0`
Prove that:
`(sinA - cosA)(1 + tanA + cotA) = secA/(cosec^2A) - (cosecA)/(sec^2A)`
If 3 `cot theta = 4 , "write the value of" ((2 cos theta - sin theta))/(( 4 cos theta - sin theta))`
Prove that secθ + tanθ =`(costheta)/(1-sintheta)`.
What is the value of (1 − cos2 θ) cosec2 θ?
The value of sin2 29° + sin2 61° is
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
Prove the following identity :
`(cot^2θ(secθ - 1))/((1 + sinθ)) = sec^2θ((1-sinθ)/(1 + secθ))`
Prove that cot θ. tan (90° - θ) - sec (90° - θ). cosec θ + 1 = 0.
Prove that sec2 (90° - θ) + tan2 (90° - θ) = 1 + 2 cot2 θ.
Prove the following identities.
sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
If `tan θ = 13/12`, then cot θ = ?
Prove that `(cos^2θ)/(sinθ) + sin θ = "cosec" θ`.
If tan α + cot α = 2, then tan20α + cot20α = ______.
If 5 tan β = 4, then `(5 sin β - 2 cos β)/(5 sin β + 2 cos β)` = ______.
