Question

show that 4 sin theta cos cube Theta - 4 cos theta sin cube theta is equal to sin 4 theta ​

Answer 1

Answer:

Sin4θ

Step-by-step explanation:

To prove --->

4 Sinθ Cos³θ - 4 Cosθ Sin³θ = Sin4θ

Proof--->

LHS = 4 Sinθ Cos³θ - 4 Cosθ Sin³θ

= 4 Sinθ Cosθ ( Cos²θ - Sin²θ )

= 2 (2Sinθ Cosθ ) (Cos²θ - Sin²θ )

We have two formulee

2SinA CosA = Sin2A

Cos²A - Sin²A = Cos2A

Applying these formula

= 2 Sin2A Cos 2A

= Sin 2 (2A )

= Sin 4A = RHS

Additional information --->

1)Cos2A = 2 Cos²A - 1

2) Cos2A = 1 - 2Sin²A

3) tan 2A = 2 tanA / (1 - tan²A)

4) Sin2A = 2 tan A / (1 + tan²A)

5) Cos2A = (1 - tan²A) /( 1 + tan²A)

Answer 2

Answer:

Hello friends Here is your answer