Question

sin 3thita=???
options are :-)

Answer 1

heya...!!!


we know that:-


sin²θ+cos²θ=1



cos(θ1+θ2)=cosθ1.cosθ2−sinθ1.sinθ2


sin(θ1+θ2)=sinθ1.cosθ2+cosθ1.sinθ2

Then


cos2θ = cos(θ+θ) = cos²θ−sin²θ


sin2θ = sin(θ+θ) = 2.sinθ.cosθ

sin3θ = sin(2θ+θ)

=> sin2θ.cosθ + cos2θ.sinθ


=> 2.sinθ.cos²θ + (cos²θ−sin²θ)×sinθ


=> 2.sinθ.(1−sin²θ) + (1 − 2.sin²θ).sinθ

=> 2sinθ - 2sin³θ + sinθ - 2sin²θ

=> 3.sinθ − 4.sin³θ


HENCE option (b) is correct