Advertisements
Advertisements
Question
Show that `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` = tan 2x
Solution
`(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
RELATED QUESTIONS
Find the values of tan(1050°)
Find the value of the trigonometric functions for the following:
cos θ = `2/3`, θ lies in the I quadrant
Find all the angles between 0° and 360° which satisfy the equation sin2θ = `3/4`
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)
Prove that sin(30° + θ) + cos(60° + θ) = cos θ
Prove that sin 105° + cos 105° = cos 45°
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
If θ is an acute angle, then find `sin (pi/4 - theta/2)`, when sin θ = `1/25`
Prove that `32(sqrt(3)) sin pi/48 cos pi/48 cos pi/24 cos pi/12 cos pi/6` = 3
Show that `cos pi/15 cos (2pi)/15 cos (3pi)/15 cos (4pi)/15 cos (5pi)/15 cos (6pi)/15 cos (7pi)/15 = 1/128`
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 sin 2A + sin 2B + sin 2C = 4 sin A sin B sin C
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 sin2A + sin2B + sin2C = 2 + 2 cos A cos B cos C
If A + B + C = 180°, prove that sin2A + sin2B − sin2C = 2 sin A sin B cos C
If A + B + C = 180°, prove that sin(B + C − A) + sin(C + A − B) + sin(A + B − C) = 4 sin A sin B sin C
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that sin2 B + sin2 C = 1
Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to
Choose the correct alternative:
If `pi < 2theta < (3pi)/2`, then `sqrt(2 + sqrt(2 + 2cos4theta)` equals to
