Question

sin θ cos 7θ cos 4θ + sin 7θ cos θ cos 4θ + sin 4θ cos 7θ cos θ = sin θ sin 4θ sin 7 θ.
prove no spam

Answer 1

Answer:

Hope it will help you

Step-by-step explanation:

1 – tan θ tan 4θ = 0, then given equation becomes

cos θ cos 4θ – sin θ sin 4θ = 0

or, (cos 3θ – cos 5θ) – (cos 5θ – cos 3θ) = 0 or,

2 (cos 3θ – cos 5θ) = 0

or, cos 3θ = cos 5θ

⇒ 5θ = 2nπ ± 3θ ……… (1) t

Taking positive sign of (1) or, 2θ = 2nπ

or, θ = nπ, where n = 0, ±1, ±2 ………

Taking negative sign of (1) or, 8θ = 2nπ

or, θ = nπ/4 where n = 0, ±1, ±2 ………

Check

Put θ = nπ in given equation 0 = 0

Put θ = nπ/4 in given equation 1/√2.1/√2 (-1) + (1/√2)(1/√2)(-1) + 0 = 0

So θ = nπ and nπ/4. Also satisfy given equation θ = nπ, nπ/4, nπ/12, where n = 0, ±1, ±2 ………

 

Answer 2

Answer:

djsbdbsmwnsnnsnsnwnnsnsb