Advertisements
Advertisements
प्रश्न
Find the value of cos 2A, A lies in the first quadrant, when cos A = `15/17`
उत्तर
we know sin2A + cos2A = 1
sin2A = 1 – cos2A
= `1 - (15/17)^2`
= `1 - 225/289`
= `(289 - 225)/289`
sin2A = `64/289`
sin A = `+- sqrt(64/289)`
= `+- 8/17`
Since A lies in the first quadrant, sin A is positive
∴ sin A = `8/17`
cos 2A = cos2A – sin2A
= `(15/17)^2 - 64/289`
=`225/289 - 64/289`
= `(225- 64)/289`
= `161/289`
APPEARS IN
संबंधित प्रश्न
Find the value of the trigonometric functions for the following:
cos θ = `- 2/3`, θ lies in the IV quadrant
Find the value of the trigonometric functions for the following:
cos θ = `2/3`, θ lies in the I quadrant
Find the value of the trigonometric functions for the following:
sec θ = `13/5`, θ lies in the IV quadrant
If sin A = `3/5` and cos B = `9/41 0 < "A" < pi/2, 0 < "B" < pi/2`, find the value of sin(A + B)
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
Prove that cos(π + θ) = − cos θ
Prove that sin 105° + cos 105° = cos 45°
If x cos θ = `y cos (theta + (2pi)/3) = z cos (theta + (4pi)/3)`. find the value of xy + yz + zx
Prove that `tan(pi/4 + theta) tan((3pi)/4 + theta)` = – 1
Find the value of tan(α + β), given that cot α = `1/2`, α ∈ `(pi, (3pi)/2)` and sec β = `- 5/3` β ∈ `(pi/2, pi)`
If θ + Φ = α and tan θ = k tan Φ, then prove that sin(θ – Φ) = `("k" - 1)/("k" + 1)` sin α
Find the value of cos 2A, A lies in the first quadrant, when sin A = `4/5`
Prove that cos 5θ = 16 cos5θ – 20 cos3θ + 5 cos θ
If A + B = 45°, show that (1 + tan A)(1 + tan B) = 2
Express the following as a sum or difference
2 sin 10θ cos 2θ
Express the following as a product
cos 65° + cos 15°
Prove that `(sin x + sin 3x + sin 5x + sin 7x)/(cos x + cos x + cos 5x cos 7x)` = tan 4x
If A + B + C = 180°, prove that sin A + sin B + sin C = `4 cos "A"/2 cos "B"/2 cos "C"/2`
