Advertisements
Advertisements
Question
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
Solution
Now A + B + C = 180°
So B + C = 180° – A
sin(B + C – A) = sin(180° – A – A)
= sin(180° – 2A) = sin 2A
Now L.H.S = sin 2A + sin 2B + sin 2C
= 4 sin A sin B sin C ......[From (i)]
= R.H.S
APPEARS IN
RELATED QUESTIONS
If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2`, find the value of tan(x + y)
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 sin(x – y), given that sin x = `8/17` with 0 < x < `pi/2`, and cos y = `- 24/25`, x < y < `(3pi)/2`
Find the value of sin 105°
Prove that sin(45° + θ) – sin(45° – θ) = `sqrt(2) sin θ`
Show that tan 75° + cot 75° = 4
Prove that sin(A + B) sin(A – B) = sin2A – sin2B
Show that tan(45° + A) = `(1 + tan"A")/(1 - tan"A")`
Prove that cot(A + B) = `(cot "A" cot "B" - 1)/(cot "A" + cot "B")`
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 sin A = `4/5`
If θ is an acute angle, then find `sin (pi/4 - theta/2)`, when sin θ = `1/25`
If A + B = 45°, show that (1 + tan A)(1 + tan B) = 2
Prove that (1 + tan 1°)(1 + tan 2°)(1 + tan 3°) ..... (1 + tan 44°) is a multiple of 4
Express the following as a product
sin 75° sin 35°
Express the following as a product
cos 65° + cos 15°
Express the following as a product
cos 35° – cos 75°
If A + B + C = `pi/2`, prove the following sin 2A + sin 2B + sin 2C = 4 cos A cos B cos C
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:
`(sin("A" - "B"))/(cos"A" cos"B") + (sin("B" - "C"))/(cos"B" cos"C") + (sin("C" - "A"))/(cos"C" cos"A")` is
