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 sin(480°)
Find the values of cos(300°)
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)
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 tan `(7pi)/12`
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
Prove that sin 75° – sin 15° = cos 105° + cos 15°
Prove that cos(A + B) cos C – cos(B + C) cos A = sin B sin(C – A)
If x cos θ = `y cos (theta + (2pi)/3) = z cos (theta + (4pi)/3)`. find the value of xy + yz + zx
Prove that sin(A + B) sin(A – B) = sin2A – sin2B
If A + B = 45°, show that (1 + tan A)(1 + tan B) = 2
Express the following as a sum or difference
sin 4x cos 2x
Express the following as a product
sin 75° sin 35°
Prove that `sin theta/2 sin (7theta)/2 + sin (3theta)/2 sin (11theta)/2` = sin 2θ sin 5θ
Prove that `(sin(4"A" - 2"B") + sin(4"B" - 2"A"))/(cos(4"A" - 2"B") + cos(4"B" - 2"A"))` = tan(A + B)
If A + B + C = 180°, prove that cos A + cos B − cos C = `- 1 + 4cos "A"/2 cos "B"/2 sin "C"/2`
If A + B + C = 2s, then prove that sin(s – A) sin(s – B)+ sin s sin(s – C) = sin A sin B
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`
