Prove that sin15=√3-1/2√2

 Solution:- 

How to prove:-

• To prove sin15= √3-1/2√2 we have to take L.H.S that is sin15

• In the next step, put (45-30) instead of 15 at sin15, so the equation becomes sin(45-30)

• Now, remind the formula of sin(A-B)=sinA.cosB-cosA.sinB 

• Putting the above formula in sin(45-30) we get sin45.cos30-cos45.sin30

• We already know about the values of sin45,cos30,cos45,sin30 these are 1/√2, √3/2,  1/√2, 1/2 respectively.

• On solving this we get required R.H.S that is root3-1/2root2

• Hence L.H.S=R.H.S