Question

i sin 2x is equal to what?

Answer 1

tan(theta) = sin(theta) / cos(theta) = a / b. cot( theta) = 1/ ... cos(2x) = cos^2(x) - sin^2(x) = 2 cos^2(x) - 1 = 1 - 2 sin^2(x). tan(2x) = 2 tan(x)  ...

Answer 2

sin(2x)=2sinxcosxsin(2x)=2sinxcosx

This can be derived by another Trigonometric Function,

sin(2x)=sin(x+x)sin(2x)=sin(x+x)

sin(A+B)=sinAcosB+cosAsinBsin(A+B)=sinAcosB+cosAsinB

sin(x+x)=sinxcosx+cosxsinxsin(x+x)=sinxcosx+cosxsinx

=sinxcosx+sinxcosx=sinxcosx+sinxcosx

=2sinxcosx=2sinxcosx

So,

sin(2x)=2sinxcosxsin(2x)=2sinxcosx

Now, 2sixcosx2sixcosx can be written as

2sinxcosx/12sinxcosx/1

OR

2sinxcosx/sin2x+cos2x2sinxcosx/sin2x+cos2x

Dividing by cos2xcos2x

2sinxcosx/cos2x/sin2x+cos2x/cos2x2sinxcosx/cos2x/sin2x+cos2x/cos2x

On solving this gives an other solution for sin(2x)sin(2x),

=2tanx/1+tan2x=2tanx/1+tan2x

sin(2x)=2sinxcosxsin(2x)=2sinxcosxOR2tanx/1+tan2x