Advertisements
Advertisements
प्रश्न
If tan θ – sin2θ = cos2θ, then show that `sin^2θ = 1/2`.
Advertisements
उत्तर
tan θ – sin2θ = cos2θ ...[Given]
∴ tan θ = sin2θ + cos2θ
∴ tan θ = 1 ...[∵ sin2θ + cos2θ = 1]
But, tan 45° = 1
∴ tan θ = tan 45°
∴ θ = 45°
sin2θ = sin245°
= `(1/sqrt(2))^2`
= `1/2`
APPEARS IN
संबंधित प्रश्न
If cosθ + sinθ = √2 cosθ, show that cosθ – sinθ = √2 sinθ.
Express the ratios cos A, tan A and sec A in terms of sin A.
Prove the following trigonometric identities
`(1 + tan^2 theta)/(1 + cot^2 theta) = ((1 - tan theta)/(1 - cot theta))^2 = tan^2 theta`
Prove the following trigonometric identities.
`(1 + sec theta)/sec theta = (sin^2 theta)/(1 - cos theta)`
Prove the following trigonometric identities.
(1 + cot A − cosec A) (1 + tan A + sec A) = 2
Prove the following trigonometric identities.
sin2 A cos2 B − cos2 A sin2 B = sin2 A − sin2 B
Prove that
`sqrt((1 + sin θ)/(1 - sin θ)) + sqrt((1 - sin θ)/(1 + sin θ)) = 2 sec θ`
If x = a sec θ cos ϕ, y = b sec θ sin ϕ and z = c tan θ, show that `x^2/a^2 + y^2/b^2 - x^2/c^2 = 1`
Prove the following identities:
(1 + cot A – cosec A)(1 + tan A + sec A) = 2
If `sqrt(3) sin theta = cos theta and theta ` is an acute angle, find the value of θ .
If cosec θ − cot θ = α, write the value of cosec θ + cot α.
Write True' or False' and justify your answer the following :
The value of the expression \[\sin {80}^° - \cos {80}^°\]
If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then
Prove the following identity :
`(1 + sinA)/(1 - sinA) = (cosecA + 1)/(cosecA - 1)`
Prove the following identity :
`(secA - 1)/(secA + 1) = (1 - cosA)/(1 + cosA)`
For ΔABC , prove that :
`sin((A + B)/2) = cos"C/2`
Evaluate:
sin2 34° + sin2 56° + 2 tan 18° tan 72° – cot2 30°
If A = 60°, B = 30° verify that tan( A - B) = `(tan A - tan B)/(1 + tan A. tan B)`.
`sin θ = 1/2`, then θ = ?
Prove that sec2θ – cos2θ = tan2θ + sin2θ.
