Advertisements
Advertisements
प्रश्न
Express the following as a sum or difference
cos 5θ cos 2θ
Advertisements
उत्तर
cos 5θ cos 2θ
We know
cosA cosB = `1/2`[cos(A + B) + cos(A – B)]
Take A = 5θ, B = 2θ
cos 5θ . cos 2θ = `1/2`[cos(5θ + 2θ) + cos(5θ – 2θ)]
cos 5θ . cos 2θ = `1/2`[cos 7θ + cos 3θ]
APPEARS IN
संबंधित प्रश्न
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
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)
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
Prove that sin(π + θ) = − sin θ.
Find a quadratic equation whose roots are sin 15° and cos 15°
Expand cos(A + B + C). Hence prove that cos A cos B cos C = sin A sin B cos C + sin B sin C cos A + sin C sin A cos B, if A + B + C = `pi/2`
Prove that sin(45° + θ) – sin(45° – θ) = `sqrt(2) sin θ`
Show that cos2 A + cos2 B – 2 cos A cos B cos(A + B) = sin2(A + B)
If tan x = `"n"/("n" + 1)` and tan y = `1/(2"n" + 1)`, find tan(x + y)
Find the value of tan(α + β), given that cot α = `1/2`, α ∈ `(pi, (3pi)/2)` and sec β = `- 5/3` β ∈ `(pi/2, pi)`
Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ
Show that `cot(7 1^circ/2) = sqrt(2) + sqrt(3) + sqrt(4) + sqrt(6)`
Prove that `32(sqrt(3)) sin pi/48 cos pi/48 cos pi/24 cos pi/12 cos pi/6` = 3
Express the following as a sum or difference
sin 5θ sin 4θ
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)
If A + B + C = 180°, prove that cos A + cos B − cos C = `- 1 + 4cos "A"/2 cos "B"/2 sin "C"/2`
Choose the correct alternative:
cos 1° + cos 2° + cos 3° + ... + cos 179° =
