Advertisements
Advertisements
प्रश्न
If A + B + C = 180◦, prove that sin 2A + sin 2B + sin 2C = 4 sin A sin B sin C
Advertisements
उत्तर
LHS = (sin 2A + sin 2B) + sin 2C
= 2 sin(A + B) cos(A – B) + 2 sin C cos C
[sin(A + B) = sin(180° – C) = sin C]
= 2 sin C cos(A – B) + 2 sin C cos C
= 2 sin C [cos(A – B) + cos C]
{cos C = cos[180° – (A + B)] = – cos (A + B)}
= 2 sin C [cos(A – B) – cos(A + B)]
= `2sin"C"{2sin (2"A")/2 sin (2"B")/2}`
= 4 sin A sin B sin C
= R.H.S
APPEARS IN
संबंधित प्रश्न
Find the values of sin(480°)
Find the values of tan(1050°)
Find the value of the trigonometric functions for the following:
tan θ = −2, θ lies in the II quadrant
Find the value of the trigonometric functions for the following:
sec θ = `13/5`, θ lies in the IV 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)
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
Prove that sin(30° + θ) + cos(60° + θ) = cos θ
If a cos(x + y) = b cos(x − y), show that (a + b) tan x = (a − b) cot y
Show that tan 75° + cot 75° = 4
Prove that cot(A + B) = `(cot "A" cot "B" - 1)/(cot "A" + cot "B")`
Express the following as a sum or difference
cos 5θ cos 2θ
Express the following as a product
cos 65° + cos 15°
Show that sin 12° sin 48° sin 54° = `1/8`
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 `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 ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos2 B + cos2 C = 1
Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to
Choose the correct alternative:
Let fk(x) = `1/"k" [sin^"k" x + cos^"k" x]` where x ∈ R and k ≥ 1. Then f4(x) − f6(x) =
