Advertisements
Advertisements
प्रश्न
Prove the following identities.
sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
Advertisements
उत्तर
L.H.S = sec4 θ (1 – sin4 θ) – 2 tan2 θ
= `1/cos^4 theta [1 - (sin^2 theta)^2]- 2 xx (sin^2 theta)/(cos^2 theta)`
= `1/(cos^4 theta) (1 + sin^2 theta) (1 - sin^2 theta) - 2 (sin^2 theta)/(cos^2 theta)`
= `1/(cos^4 theta) xx cos^2 theta (1 + sin^2 theta) - 2 (sin^2 theta)/(cos^2 theta)`
= `(1 + sin^2 theta)/(cos^2 theta) - (2sin^2 theta)/(cos^2 theta)`
= `(1 + sin^2 theta - 2sin^2 theta)/(cos^2 theta)`
= `(1 - sin^2 theta)/(cos^2 theta)`
= `(cos^2 theta)/(cos^2 theta)`
L.H.S = R.H.S
∴ sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`sin theta/(1 - cos theta) = cosec theta + cot theta`
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
Prove the following identity :
`sin^2Acos^2B - cos^2Asin^2B = sin^2A - sin^2B`
Prove the following identity :
`sqrt((1 + cosA)/(1 - cosA)) = cosecA + cotA`
If cosθ = `5/13`, then find sinθ.
Prove that the following identities:
Sec A( 1 + sin A)( sec A - tan A) = 1.
If sin θ + cos θ = `sqrt(3)`, then prove that tan θ + cot θ = 1.
If sin θ (1 + sin2 θ) = cos2 θ, then prove that cos6 θ – 4 cos4 θ + 8 cos2 θ = 4
Prove that `1/("cosec" θ - cot θ) = "cosec" θ + cot θ`.
If cos A + cos2A = 1, then sin2A + sin4A = ?
