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 `tan ((19pi)/3)`
Find the value of the trigonometric functions for the following:
cos θ = `2/3`, θ lies in the I quadrant
Find the value of the trigonometric functions for the following:
tan θ = −2, θ lies in the II quadrant
Find all the angles between 0° and 360° which satisfy the equation sin2θ = `3/4`
If sin A = `3/5` and cos B = `9/41 0 < "A" < pi/2, 0 < "B" < pi/2`, find the value of sin(A + B)
Find the value of cos 105°.
Find a quadratic equation whose roots are sin 15° and cos 15°
Prove that sin(30° + θ) + cos(60° + θ) = cos θ
Prove that sin(n + 1) θ sin(n – 1) θ + cos(n + 1) θ cos(n – 1)θ = cos 2θ, n ∈ Z
Prove that sin(A + B) sin(A – B) = sin2A – sin2B
Prove that cos(A + B) cos(A – B) = cos2A – sin2B = cos2B – sin2A
Prove that cos 8θ cos 2θ = cos25θ – sin23θ
If θ + Φ = α and tan θ = k tan Φ, then prove that sin(θ – Φ) = `("k" - 1)/("k" + 1)` sin α
If θ is an acute angle, then find `cos (pi/4 + theta/2)`, when sin θ = `8/9`
Prove that cos 5θ = 16 cos5θ – 20 cos3θ + 5 cos θ
Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ
Prove that 1 + cos 2x + cos 4x + cos 6x = 4 cos x cos 2x cos 3x
Show that cot(A + 15°) – tan(A – 15°) = `(4cos2"A")/(1 + 2 sin2"A")`
Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to
