Question

x
How to prove sin3A interms of A​

Answer 1

Answer:

3sinA-4sin^3A

Step-by-step explanation:

If A is number or angle then we have,

sin3A=3 sinA-4sin^3A

sin(2A+A)

sin2AcosA+cos2AsinA

2sinAcosA.cosA+(1-2sin^2A)sinA

2sinA(1-sin^2A)+sinA-2sin^3A

2sinA-2sin^3A+sinA-2sin^3A

3sinA-4sin^3A

proved.

Answer 2

Answer:sin3A=3SinA-4Sin^3A

Step-by-step explanation:

Let Sin3A=Sin(A+2A)

Now we know that,

Sin(A+2A)+Sin(A-2A)=2SinACos(2A)

Or, Sin(3A)-SinA=2SinACos(2A)

Or, Sin(3A)=2SinACos(2A)+SinA

Again we know,

Cos(2A)=1-2Sin^2(A)

Now,

Sin(3A)=2SinA{1-2Sin^2(A)}+SinA

=2SinA-4Sin^3(A)+SinA

=3SinA-4Sin^3(A)