Advertisements
Advertisements
प्रश्न
Prove that `(sin x + sin 3x + sin 5x + sin 7x)/(cos x + cos x + cos 5x cos 7x)` = tan 4x
Advertisements
उत्तर
Nr: (sin x + sin 7x) + (sin 3x + sin 5x)
= `[2sin (7x + x)/2 cos (7x - x)/2] + [2sin (5x + 3x)/2 cos (5x - 3x)/2]`
= 2 sin 4x cos 3x + 2 sin 4x cos x
= 2 sin 4x (cos 3x + cos x) .....(1)
Dr. (cos x + cos 7x) + (cos 3x + cos 5x)
= `[2cos (7x + x)/2 cos (7x - x)/2] + [2cos (5x + 3x)/2 cos (5x - 3x)/2]`
= 2 cos 4x cos 3x + 2 cos 4x cosx
= 2 cos 4x (cos 3x + cos x) .....(2)
L.H.S = `((1))/((2))`
= `(2sin 4x(cos 3x + cos x))/(2cos 4x(cos 3x + cos x))`
= tan 4x
= R.H.S
APPEARS IN
संबंधित प्रश्न
Find the values of sin(480°)
Find the values of sin (– 1110°)
Find the values of `tan ((19pi)/3)`
Find the value of the trigonometric functions for the following:
tan θ = −2, θ lies in the II quadrant
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 a quadratic equation whose roots are sin 15° and cos 15°
Show that tan 75° + cot 75° = 4
Prove that sin(n + 1) θ sin(n – 1) θ + cos(n + 1) θ cos(n – 1)θ = cos 2θ, n ∈ Z
Prove that sin2(A + B) – sin2(A – B) = sin2A sin2B
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 A + B = 45°, show that (1 + tan A)(1 + tan B) = 2
Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ
Express the following as a product
cos 65° + cos 15°
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 = 180°, prove that sin A + sin B + sin C = `4 cos "A"/2 cos "B"/2 cos "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
Choose the correct alternative:
`(1 + cos pi/8) (1 + cos (3pi)/8) (1 + cos (5pi)/8) (1 + cos (7pi)/8)` =
