Advertisements
Advertisements
प्रश्न
Show that `((cos theta -cos 3theta)(sin 8theta + sin 2theta))/((sin 5theta - sin theta) (cos 4theta - cos 6theta))` = 1
Advertisements
उत्तर
`((cos theta -cos 3theta)(sin 8theta + sin 2theta))/((sin 5theta - sin theta) (cos 4theta - cos 6theta)) = ((cos 3theta -cos theta)(sin 8theta + sin 2theta))/((sin 5theta - sin theta) (cos 6theta - cos 4theta))`
= `(2sin((3theta + theta)/2) sin ((theta - 3theta)/2) * 2sin((8theta + 20)/2) cos((8theta - 2theta)/2))/((2cos((5theta + theta)/2) * sin((5theta - theta)/2) * 2sin((6theta - 4theta)/2) sin((4theta - 6theta)/2)`
= `(sin 2theta* sin(- theta) *sin 5theta * cos 3theta)/(cos3theta * sin 2theta * sin 5theta * sin (- theta))`
= 1
APPEARS IN
संबंधित प्रश्न
Find the values of sin (– 1110°)
Find the values of `tan ((19pi)/3)`
Find the values of `sin (-(11pi)/3)`
Find the value of the trigonometric functions for the following:
cos θ = `- 1/2`, θ lies in the III quadrant
Find the value of the trigonometric functions for the following:
cos θ = `- 2/3`, θ lies in the IV quadrant
Find the value of the trigonometric functions for the following:
sec θ = `13/5`, θ lies in the IV quadrant
Prove that `(cot(180^circ + theta) sin(90^circ - theta) cos(- theta))/(sin(270^circ + theta) tan(- theta) "cosec"(360^circ + theta))` = cos2θ cotθ
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)
Find the value of tan `(7pi)/12`
Find a quadratic equation whose roots are sin 15° and cos 15°
Prove that sin(30° + θ) + cos(60° + θ) = cos θ
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 `sin (pi/4 - theta/2)`, when sin θ = `1/25`
Prove that cos 5θ = 16 cos5θ – 20 cos3θ + 5 cos θ
Express the following as a sum or difference
sin 35° cos 28°
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`
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 = `pi/2`, prove the following cos 2A + cos 2B + cos 2C = 1 + 4 sin A sin B sin C
