Question

Sin3A =3sinA-4sin^3A​

Answer 1

Answer:

3sin-4sin^3 a

Step-by-step explanation:

sin(2a+a)

=sin2a.cosa+cos2a.sina

=2sina.cosa.cosa+(cos^2 a-sin^2a)sina

=2sina.cos^2 a+sina-2sin^3a

=2sina(1-sin^2a)+sina-2sin^3 a

=2sina-2sin^3a+sina-2sin^3a

=3sin-4sin^3 a

Answer 2

Step-by-step explanation:

sin(3a)

we can also write it as,

sin(2a+a)

using identity sin(a+b)= sina cosb + cosa sinb

=sin2a.cosa+cos2a.sina

now here we use formula sin2A = 2sinacosa and

cos2a = cos²a-sin²a putting these value in eq we get,

=2sina.cosa.cosa+(cos²a-sin²a)sina

=2sina.cos² a+sina-2sin³a

=2sina(1-sin²a)+sina-2sin³ a

=2sina-2sin³a+sina-2sin³a

=3sin-4sin³a