Advertisements
Advertisements
प्रश्न
Prove that sin x + sin 2x + sin 3x = sin 2x (1 + 2 cos x)
Advertisements
उत्तर
sin x + sin 2x + sin 3x = sin x + 2 sin x cos x + 3 sin x – 4 sin3 x
= sin x [1 + 2 cos x + 3 – 4 sin2 x]
= sin x [2 cos x + 4 – 4 sin2 x ]
= sin x [2 cosx + 4(1 – sin2x)]
= sin x [2 cos x + 4 cos2x]
= 2 sin x cos x [1 + 2 cos x]
= sin 2x (1 + 2 cosx)
APPEARS IN
संबंधित प्रश्न
Find the values of cot(660°)
Find the values of `tan ((19pi)/3)`
Find all the angles between 0° and 360° which satisfy the equation sin2θ = `3/4`
If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2` find the value of sin(x + y)
Find cos(x − y), given that cos x = `- 4/5` with `pi < x < (3pi)/2` and sin y = `- 24/25` with `pi < y < (3pi)/2`
Find the value of cos 105°.
Prove that cos(π + θ) = − cos θ
Prove that sin(π + θ) = − sin θ.
Prove that sin 75° – sin 15° = cos 105° + cos 15°
Find the value of cos 2A, A lies in the first quadrant, when cos A = `15/17`
If cos θ = `1/2 ("a" + 1/"a")`, show that cos 3θ = `1/2 ("a"^3 + 1/"a"^3)`
If A + B = 45°, show that (1 + tan A)(1 + tan B) = 2
Express the following as a product
sin 50° + sin 40°
Prove that cos(30° – A) cos(30° + A) + cos(45° – A) cos(45° + A) = `cos 2"A" + 1/4`
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)`
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos B – cos C = `- 1 + 2sqrt(2) cos "B"/2 sin "C"/2`
Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to
Choose the correct alternative:
`(1 + cos pi/8) (1 + cos (3pi)/8) (1 + cos (5pi)/8) (1 + cos (7pi)/8)` =
