Advertisements
Advertisements
Question
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
Advertisements
Solution
cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
cos(30° + x) = cos 30°. cos x – sin 30° sin x
= `sqrt(3)/2 cos x - 1/2 sin x`
cos(30° + x) = `(sqrt(3)cosx- sinx)/2`
APPEARS IN
RELATED QUESTIONS
Find the values of tan(1050°)
Find the value of the trigonometric functions for the following:
cos θ = `2/3`, θ lies in the I quadrant
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 tan(x + y)
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)
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 sin(x – y), given that sin x = `8/17` with 0 < x < `pi/2`, and cos y = `- 24/25`, x < y < `(3pi)/2`
Find the value of cos 105°.
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(n + 1) θ sin(n – 1) θ + cos(n + 1) θ cos(n – 1)θ = cos 2θ, n ∈ Z
Prove that cos 8θ cos 2θ = cos25θ – sin23θ
Show that tan(45° + A) = `(1 + tan"A")/(1 - tan"A")`
Prove that (1 + sec 2θ)(1 + sec 4θ) ... (1 + sec 2nθ) = tan 2nθ
Show that sin 12° sin 48° sin 54° = `1/8`
Prove that sin x + sin 2x + sin 3x = sin 2x (1 + 2 cos x)
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 sin2A + sin2B − sin2C = 2 sin A sin B cos C
If A + B + C = `pi/2`, prove the following sin 2A + sin 2B + sin 2C = 4 cos A cos B cos C
Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to
