Advertisements
Advertisements
Question
Show that `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` = tan 2x
Advertisements
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 `sin (-(11pi)/3)`
Prove that `(cot(180^circ + theta) sin(90^circ - theta) cos(- theta))/(sin(270^circ + theta) tan(- theta) "cosec"(360^circ + theta))` = cos2θ cotθ
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
Prove that sin 105° + cos 105° = cos 45°
Prove that sin 75° – sin 15° = cos 105° + cos 15°
Show that tan 75° + cot 75° = 4
Prove that cos 8θ cos 2θ = cos25θ – sin23θ
Find the value of cos 2A, A lies in the first quadrant, when cos A = `15/17`
Prove that (1 + tan 1°)(1 + tan 2°)(1 + tan 3°) ..... (1 + tan 44°) is a multiple of 4
Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ
Prove that (1 + sec 2θ)(1 + sec 4θ) ... (1 + sec 2nθ) = tan 2nθ
Express the following as a product
sin 75° sin 35°
Show that `((cos theta -cos 3theta)(sin 8theta + sin 2theta))/((sin 5theta - sin theta) (cos 4theta - cos 6theta))` = 1
Prove that sin x + sin 2x + sin 3x = sin 2x (1 + 2 cos x)
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
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
Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to
