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 value of the trigonometric functions for the following:
cos θ = `2/3`, θ lies in the I quadrant
If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2`, find the value of cos(x − y)
Find the value of cos 105°.
Prove that cos(π + θ) = − cos θ
Prove that sin(π + θ) = − sin θ.
Prove that sin(30° + θ) + cos(60° + θ) = cos θ
Prove that sin 105° + cos 105° = cos 45°
Prove that `tan(pi/4 + theta) tan((3pi)/4 + theta)` = – 1
If θ + Φ = α and tan θ = k tan Φ, then prove that sin(θ – Φ) = `("k" - 1)/("k" + 1)` sin α
If cos θ = `1/2 ("a" + 1/"a")`, show that cos 3θ = `1/2 ("a"^3 + 1/"a"^3)`
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 product
cos 65° + cos 15°
Prove that cos(30° – A) cos(30° + A) + cos(45° – A) cos(45° + A) = `cos 2"A" + 1/4`
If A + B + C = 180°, prove that cos A + cos B − cos C = `- 1 + 4cos "A"/2 cos "B"/2 sin "C"/2`
If A + B + C = 2s, then prove that sin(s – A) sin(s – B)+ sin s sin(s – C) = sin A sin B
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)`
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that sin2 B + sin2 C = 1
Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to
