Advertisements
Advertisements
प्रश्न
Find the value of cos 2A, A lies in the first quadrant, when cos A = `15/17`
Advertisements
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 values of tan(1050°)
`(5/7, (2sqrt(6))/7)` is a point on the terminal side of an angle θ in standard position. Determine the six trigonometric function values of angle θ
Show that `sin^2 pi/18 + sin^2 pi/9 + sin^2 (7pi)/18 + sin^2 (4pi)/9` = 2
If sin A = `3/5` and cos B = `9/41, 0 < "A" < pi/2, 0 < "B" < pi/2`, find the value of cos(A – B)
Prove that cos(π + θ) = − cos θ
Find a quadratic equation whose roots are sin 15° and cos 15°
Prove that sin(30° + θ) + cos(60° + 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
Show that tan(45° + A) = `(1 + tan"A")/(1 - tan"A")`
If tan x = `"n"/("n" + 1)` and tan y = `1/(2"n" + 1)`, find tan(x + y)
Find the value of cos 2A, A lies in the first quadrant, when tan A `16/63`
If θ is an acute angle, then find `sin (pi/4 - theta/2)`, when sin θ = `1/25`
If θ is an acute angle, then find `cos (pi/4 + theta/2)`, when sin θ = `8/9`
Show that `cot(7 1^circ/2) = sqrt(2) + sqrt(3) + sqrt(4) + sqrt(6)`
Prove that `32(sqrt(3)) sin pi/48 cos pi/48 cos pi/24 cos pi/12 cos pi/6` = 3
Express the following as a sum or difference
sin 5θ sin 4θ
If A + B + C = 180°, prove that sin2A + sin2B + sin2C = 2 + 2 cos A cos B cos C
If x + y + z = xyz, then prove that `(2x)/(1 - x^2) + (2y)/(1 - y^2) + (2z)/(1 - z^2) = (2x)/(1 - x^2) (2y)/(1 - y^2) (2z)/(1 - z^2)`
Choose the correct alternative:
`(sin("A" - "B"))/(cos"A" cos"B") + (sin("B" - "C"))/(cos"B" cos"C") + (sin("C" - "A"))/(cos"C" cos"A")` is
