Advertisements
Advertisements
प्रश्न
\[\frac{1 + \tan^2 A}{1 + \cot^2 A}\]is equal to
पर्याय
sec2 A
−1
cot2 A
tan2 A
Advertisements
उत्तर
Given:
`(1+tan^2 A)/(1+cot^2 A)`
`= (1+sin^2 A/cos^2 A)/(1+cos^2/sin^2A)`
`=(cos^2 A+sin^2 A/cos^2 A)/(sin^2 A+cos^2 A/sin^2A)`
`=(1/cos^2 A)/(1/sin^2A)`
`=sin^2 A/cos^2 A`
`= tan^2 A`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(cos^2 theta)/sin theta - cosec theta + sin theta = 0`
Prove the following identities:
`(1+ sin A)/(cosec A - cot A) - (1 - sin A)/(cosec A + cot A) = 2(1 + cot A)`
Prove that:
2 sin2 A + cos4 A = 1 + sin4 A
Prove the following identities:
`cot^2A((secA - 1)/(1 + sinA)) + sec^2A((sinA - 1)/(1 + secA)) = 0`
If `( cosec theta + cot theta ) =m and ( cosec theta - cot theta ) = n, ` show that mn = 1.
If `( sin theta + cos theta ) = sqrt(2) , " prove that " cot theta = ( sqrt(2)+1)`.
If `( cos theta + sin theta) = sqrt(2) sin theta , " prove that " ( sin theta - cos theta ) = sqrt(2) cos theta`
Write the value of ` cosec^2 (90°- theta ) - tan^2 theta`
Prove the following identity :
secA(1 + sinA)(secA - tanA) = 1
Prove the following identity :
`sin^2Acos^2B - cos^2Asin^2B = sin^2A - sin^2B`
Prove the following identity :
`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`
Prove the following identity :
`(tanθ + 1/cosθ)^2 + (tanθ - 1/cosθ)^2 = 2((1 + sin^2θ)/(1 - sin^2θ))`
Prove that: 2(sin6 θ + cos6 θ) – 3 (sin4 θ + cos4 θ) + 1 = 0.
Prove that `(sin θ. cos (90° - θ) cos θ)/sin( 90° - θ) + (cos θ sin (90° - θ) sin θ)/(cos(90° - θ)) = 1`.
Prove that `cot^2 "A" [(sec "A" - 1)/(1 + sin "A")] + sec^2 "A" [(sin"A" - 1)/(1 + sec"A")]` = 0
cos 45° = ?
Which is not correct formula?
If 2 cos θ + sin θ = `1(θ ≠ π/2)`, then 7 cos θ + 6 sin θ is equal to ______.
`(cos^2 θ)/(sin^2 θ) - 1/(sin^2 θ)`, in simplified form, is ______.
