prove sin2x=2tanx/1+tan^2x

Question

prove LHS to RHS not RHS to LHS , and pls keep it simple

Answer 1

Check the supposed identity by substituting a value for x. Let x=30°, then sin(2x)=√3/2, tan(x)=1/√3. The RHS becomes:

(2/√3)/(1+⅓)=(2/√3)/(4/3)=(2/√3)(3/4)=√3/2, so the identity appears to be true.

sin(2x)=2sin(x)cos(x)=

2(sin(x)/cos(x))cos²(x)=

2tan(x)/sec²(x)=

2tan(x)/(1+tan²(x)) QED

[sin²(x)+cos²(x)=1, so, dividing through by cos²(x):

tan²(x)+1=sec²(x)]