Advertisements
Advertisements
प्रश्न
Prove that `(sin 4x + sin 2x)/(cos 4x + cos 2x)` = tan 3x
Advertisements
उत्तर
`(sin 4x + sin 2x)/(cos 4x + cos 2x)` = `(2sin((4xx + 2x)/2) * cos((4x - 2x)/2))/(2cos((4x + 2x)/2) * cos((4x - 2x)/2))`
= `(sin 3x * cos x)/(cos 3x * cos x)`
= `(sin 3x)/(cos 3x)`
= tan 3x
APPEARS IN
संबंधित प्रश्न
Find the values of sin (– 1110°)
Find the value of the trigonometric functions for the following:
tan θ = −2, θ lies in the II quadrant
Find the value of the trigonometric functions for the following:
sec θ = `13/5`, θ lies in the IV quadrant
Show that `sin^2 pi/18 + sin^2 pi/9 + sin^2 (7pi)/18 + sin^2 (4pi)/9` = 2
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 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`
Find the value of tan `(7pi)/12`
Prove that sin(π + θ) = − sin θ.
Find a quadratic equation whose roots are sin 15° and cos 15°
Prove that sin(n + 1) θ sin(n – 1) θ + cos(n + 1) θ cos(n – 1)θ = cos 2θ, n ∈ Z
Prove that `32(sqrt(3)) sin pi/48 cos pi/48 cos pi/24 cos pi/12 cos pi/6` = 3
Express the following as a sum or difference
2 sin 10θ cos 2θ
Express the following as a product
sin 75° sin 35°
Express the following as a product
sin 50° + sin 40°
If A + B + C = 180°, prove that sin2A + sin2B + sin2C = 2 + 2 cos A cos B cos C
If A + B + C = 180°, prove that sin A + sin B + sin C = `4 cos "A"/2 cos "B"/2 cos "C"/2`
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos2 B + cos2 C = 1
