Advertisements
Advertisements
Question
Express the following as a product
sin 50° + sin 40°
Advertisements
Solution
We know sin C + sin D = `2 sin ("C" + "D")/2 * cos ("C" - "D")/2`
Take C = 50°, D = 40°
sin 50° + sin 40° = `2sin((50^circ + 40^circ)/2) * cos((50^circ - 40^circ)/2)`
sin 50° + sin 40° = `2cos(90^circ/2) * cos(10^circ/2)`
sin 50° + sin 40° = 2 cos(45°) . cos(5°)
APPEARS IN
RELATED QUESTIONS
Find the values of tan(1050°)
Find the value of the trigonometric functions for the following:
cos θ = `- 1/2`, θ lies in the III quadrant
Show that `sin^2 pi/18 + sin^2 pi/9 + sin^2 (7pi)/18 + sin^2 (4pi)/9` = 2
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 cos(x − y), given that cos x = `- 4/5` with `pi < x < (3pi)/2` and sin y = `- 24/25` with `pi < y < (3pi)/2`
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
Show that tan 75° + cot 75° = 4
Find the value of cos 2A, A lies in the first quadrant, when tan A `16/63`
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
If A + B = 45°, show that (1 + tan A)(1 + tan B) = 2
Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ
Express the following as a sum or difference
sin 4x cos 2x
Show that `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` = tan 2x
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 = 180°, prove that sin(B + C − A) + sin(C + A − B) + sin(A + B − C) = 4 sin A sin B sin C
If x + y + z = xyz, then prove that `(2x)/(1 - x^2) + (2y)/(1 - y^2) + (2z)/(1 - z^2) = (2x)/(1 - x^2) (2y)/(1 - y^2) (2z)/(1 - z^2)`
Choose the correct alternative:
`(1 + cos pi/8) (1 + cos (3pi)/8) (1 + cos (5pi)/8) (1 + cos (7pi)/8)` =
