Advertisements
Advertisements
प्रश्न
Prove that sin 4α = `4 tan alpha (1 - tan^2alpha)/(1 + tan^2 alpha)^2`
Advertisements
उत्तर
sin 4α = sin 2(2α)
= `(2tan(2alpha))/(1 + tan^2 (2alpha))`
= `(2((2tan alpha)/(1 - tan^2 alpha)))/(1 + ((2 tan alpha)/(1 - tan^2 alpha))^2`
= `((4 tan alpha)/(1 - tan^2 alpha))/(((1 - tan^2 alpha)^2 + 4 tan^2 alpha)/(1 - tan^2 alpha)^2)`
= `(4 tan alpha (1 - tan^2 alpha))/(1 + tan^2 alpha - 2 tan^2 alpha + 4 tan^2 alpha)`
= `(4 tan alpha (1 - tan^2 alpha))/(1 + 2 tan^2 alpha + tan^4 alpha)`
sin 4α = `(4 tan alpha (1 - tan^2 alpha))/(1 + tan^2 alpha)^2`
APPEARS IN
संबंधित प्रश्न
Find the values of cos(300°)
Find the values of `sin (-(11pi)/3)`
Find all the angles between 0° and 360° which satisfy the equation sin2θ = `3/4`
If sin A = `3/5` and cos B = `9/41 0 < "A" < pi/2, 0 < "B" < pi/2`, find the value of sin(A + B)
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
Prove that cos(π + θ) = − cos θ
Expand cos(A + B + C). Hence prove that cos A cos B cos C = sin A sin B cos C + sin B sin C cos A + sin C sin A cos B, if A + B + C = `pi/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)
Prove that `tan(pi/4 + theta) tan((3pi)/4 + theta)` = – 1
If θ + Φ = α and tan θ = k tan Φ, then prove that sin(θ – Φ) = `("k" - 1)/("k" + 1)` sin α
Find the value of cos 2A, A lies in the first quadrant, when tan A `16/63`
Prove that (1 + tan 1°)(1 + tan 2°)(1 + tan 3°) ..... (1 + tan 44°) is a multiple of 4
Express the following as a sum or difference
sin 4x cos 2x
Express the following as a sum or difference
sin 5θ sin 4θ
Show that `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` = tan 2x
Choose the correct alternative:
`1/(cos 80^circ) - sqrt(3)/(sin 80^circ)` =
