Advertisements
Advertisements
प्रश्न
If A + B + C = `pi/2`, prove the following sin 2A + sin 2B + sin 2C = 4 cos A cos B cos C
Advertisements
उत्तर
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
संबंधित प्रश्न
Prove that `(cot(180^circ + theta) sin(90^circ - theta) cos(- theta))/(sin(270^circ + theta) tan(- theta) "cosec"(360^circ + theta))` = cos2θ cotθ
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 sin(x + y)
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)
Prove that sin(π + θ) = − sin θ.
Show that tan(45° − A) = `(1 - tan "A")/(1 + tan "A")`
If θ + Φ = α and tan θ = k tan Φ, then prove that sin(θ – Φ) = `("k" - 1)/("k" + 1)` sin α
Prove that cos 5θ = 16 cos5θ – 20 cos3θ + 5 cos θ
Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ
Express the following as a sum or difference
sin 35° cos 28°
Express the following as a product
sin 75° sin 35°
Express the following as a product
cos 35° – cos 75°
Show that sin 12° sin 48° sin 54° = `1/8`
Show that `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` = tan 2x
Prove that `(sin(4"A" - 2"B") + sin(4"B" - 2"A"))/(cos(4"A" - 2"B") + cos(4"B" - 2"A"))` = tan(A + B)
If A + B + C = 180°, prove that `tan "A"/2 tan "B"/2 + tan "B"/2 tan "C"/2 + tan "C"/2 tan "A"/2` = 1
If A + B + C = 180°, prove that sin A + sin B + sin C = `4 cos "A"/2 cos "B"/2 cos "C"/2`
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 A + B + C = `pi/2`, prove the following cos 2A + cos 2B + cos 2C = 1 + 4 sin A sin B sin C
Choose the correct alternative:
`1/(cos 80^circ) - sqrt(3)/(sin 80^circ)` =
