Advertisements
Advertisements
Question
If A + B + C = `pi/2`, prove the following sin 2A + sin 2B + sin 2C = 4 cos A cos B cos C
Advertisements
Solution
L.H.S = (sin 2A + sin 2B) + sin 2C
= 2 sin(A + B) cos(A – B) + 2 sin C cos C
= 2 sin(90° – C) cos(A – B) + 2 sin C cos C
= 2 cos C [cos (A – B) + sin C] + cos(A + B) .....(∴ A + B = `π/2` – C)
= 2 cos C [cos(A – B) + cos(A + B)]
= 2 cos C [2 cos A cos B]
= 4 cos A cos B cos C
= R.H.S
APPEARS IN
RELATED QUESTIONS
Find the values of `tan ((19pi)/3)`
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 cos(x − y), given that cos x = `- 4/5` with `pi < x < (3pi)/2` and sin y = `- 24/25` with `pi < y < (3pi)/2`
Find the value of tan `(7pi)/12`
Prove that sin(π + θ) = − sin θ.
If tan x = `"n"/("n" + 1)` and tan y = `1/(2"n" + 1)`, find tan(x + y)
If θ + Φ = α and tan θ = k tan Φ, then prove that sin(θ – Φ) = `("k" - 1)/("k" + 1)` sin α
Find the value of cos 2A, A lies in the first quadrant, when cos A = `15/17`
If cos θ = `1/2 ("a" + 1/"a")`, show that cos 3θ = `1/2 ("a"^3 + 1/"a"^3)`
Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ
Express the following as a product
cos 35° – cos 75°
Show that sin 12° sin 48° sin 54° = `1/8`
Show that `((cos theta -cos 3theta)(sin 8theta + sin 2theta))/((sin 5theta - sin theta) (cos 4theta - cos 6theta))` = 1
Prove that `(sin 4x + sin 2x)/(cos 4x + cos 2x)` = tan 3x
If A + B + C = 180°, prove that sin A + sin B + sin C = `4 cos "A"/2 cos "B"/2 cos "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 ∆ABC is a right triangle and if ∠A = `pi/2` then prove that sin2 B + sin2 C = 1
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos B – cos C = `- 1 + 2sqrt(2) cos "B"/2 sin "C"/2`
Choose the correct alternative:
`(sin("A" - "B"))/(cos"A" cos"B") + (sin("B" - "C"))/(cos"B" cos"C") + (sin("C" - "A"))/(cos"C" cos"A")` is
