Advertisements
Advertisements
प्रश्न
Show that `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` = tan 2x
Advertisements
उत्तर
`(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x) = (1/2 [sin 9x + sin 7x] - 1/2 [sin 9x + sin 3x])/(1/2 [cos 3x + cos x] - 1/2 [cos x - cos 3x])`
= `(sin 9x + sin 7x - sin 9x - sin 3x)/(cos 3x + cos x - cos x + cos 7x)`
= `(sin 7x - sin 3x)/(cos 3x + cos 7x)`
= `(sin 7x - sin 3x)/(cos 7x + cos 3x)`
= `(2cos((7x + 3x)/2) * sin ((7x 3x)/2))/(2cos((7x + 3x)/2) * cos((7x - 3x)/2)`
= `(2 cos 5x * sin 2x)/(2 cos 5x * cos 2x)`
= `(sin 2x)/(cos 2x)`
= tan 2x
APPEARS IN
संबंधित प्रश्न
Find the values of sin(480°)
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)
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`
If x cos θ = `y cos (theta + (2pi)/3) = z cos (theta + (4pi)/3)`. find the value of xy + yz + zx
Prove that sin2(A + B) – sin2(A – B) = sin2A sin2B
If cos(α – β) + cos(β – γ) + cos(γ – α) = `- 3/2`, then prove that cos α + cos β + cos γ = sin α + sin β + sin γ = 0
Show that tan(45° + A) = `(1 + tan"A")/(1 - tan"A")`
Find the value of cos 2A, A lies in the first quadrant, when tan A `16/63`
Prove that (1 + sec 2θ)(1 + sec 4θ) ... (1 + sec 2nθ) = tan 2nθ
Express the following as a sum or difference
sin 4x cos 2x
Express the following as a sum or difference
2 sin 10θ cos 2θ
Express the following as a product
cos 35° – cos 75°
Prove that `(sin x + sin 3x + sin 5x + sin 7x)/(cos x + cos x + cos 5x cos 7x)` = tan 4x
If A + B + C = 180°, prove that sin2A + sin2B + sin2C = 2 + 2 cos A cos B cos C
Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to
Choose the correct alternative:
Let fk(x) = `1/"k" [sin^"k" x + cos^"k" x]` where x ∈ R and k ≥ 1. Then f4(x) − f6(x) =
Choose the correct alternative:
`(sin("A" - "B"))/(cos"A" cos"B") + (sin("B" - "C"))/(cos"B" cos"C") + (sin("C" - "A"))/(cos"C" cos"A")` is
