Advertisements
Advertisements
Question
Prove that `(sin 4x + sin 2x)/(cos 4x + cos 2x)` = tan 3x
Advertisements
Solution
`(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
RELATED QUESTIONS
Find the values of sin(480°)
Find the values of `tan ((19pi)/3)`
Find all the angles between 0° and 360° which satisfy the equation sin2θ = `3/4`
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 75° – sin 15° = cos 105° + cos 15°
If x cos θ = `y cos (theta + (2pi)/3) = z cos (theta + (4pi)/3)`. find the value of xy + yz + zx
Prove that sin(A + B) sin(A – B) = sin2A – sin2B
Show that cos2 A + cos2 B – 2 cos A cos B cos(A + B) = sin2(A + B)
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 tan x = `"n"/("n" + 1)` and tan y = `1/(2"n" + 1)`, find tan(x + y)
If θ is an acute angle, then find `cos (pi/4 + theta/2)`, when sin θ = `8/9`
Show that `((cos theta -cos 3theta)(sin 8theta + sin 2theta))/((sin 5theta - sin theta) (cos 4theta - cos 6theta))` = 1
Prove that `sin theta/2 sin (7theta)/2 + sin (3theta)/2 sin (11theta)/2` = sin 2θ sin 5θ
Show that cot(A + 15°) – tan(A – 15°) = `(4cos2"A")/(1 + 2 sin2"A")`
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 `tan "A"/2 tan "B"/2 + tan "B"/2 tan "C"/2 + tan "C"/2 tan "A"/2` = 1
If A + B + C = 180°, prove that sin A + sin B + sin C = `4 cos "A"/2 cos "B"/2 cos "C"/2`
If A + B + C = 2s, then prove that sin(s – A) sin(s – B)+ sin s sin(s – C) = sin A sin B
Choose the correct alternative:
`1/(cos 80^circ) - sqrt(3)/(sin 80^circ)` =
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) =
