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 tan(1050°)
Find the values of cot(660°)
Prove that `(cot(180^circ + theta) sin(90^circ - theta) cos(- theta))/(sin(270^circ + theta) tan(- theta) "cosec"(360^circ + theta))` = cos2θ cotθ
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)
If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2`, find the value of cos(x − y)
If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2`, find the value of tan(x + y)
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 sin(x – y), given that sin x = `8/17` with 0 < x < `pi/2`, and cos y = `- 24/25`, x < y < `(3pi)/2`
Prove that sin(A + B) sin(A – B) = sin2A – sin2B
Show that tan(45° − A) = `(1 - tan "A")/(1 + tan "A")`
If θ + Φ = α and tan θ = k tan Φ, then prove that sin(θ – Φ) = `("k" - 1)/("k" + 1)` sin α
If θ is an acute angle, then find `cos (pi/4 + theta/2)`, when sin θ = `8/9`
Prove that sin 4α = `4 tan alpha (1 - tan^2alpha)/(1 + tan^2 alpha)^2`
Show that sin 12° sin 48° sin 54° = `1/8`
Show that `((cos theta -cos 3theta)(sin 8theta + sin 2theta))/((sin 5theta - sin theta) (cos 4theta - cos 6theta))` = 1
Prove that cos(30° – A) cos(30° + A) + cos(45° – A) cos(45° + A) = `cos 2"A" + 1/4`
If A + B + C = 180°, prove that `tan "A"/2 tan "B"/2 + tan "B"/2 tan "C"/2 + tan "C"/2 tan "A"/2` = 1
If A + B + C = `pi/2`, prove the following sin 2A + sin 2B + sin 2C = 4 cos A cos B cos C
If A + B + C = `pi/2`, prove the following cos 2A + cos 2B + cos 2C = 1 + 4 sin A sin B sin C
Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to
