Question

Sin 120° + COS75° = 3✓5/2 (Prove this)​

Answer 1

Sin 120° = Sin (180-60)

             = Sin60°

             = $\frac{\sqrt{3} }{2}$

Cos 75° = Cos (30+45)°

             = Cos30°×Cos45° - Sin30°×Sin45°

             = $\frac{\sqrt{3} }{2}*\frac{1}{\sqrt{2} } - \frac{1}{2} *\frac{1}{\sqrt{2} }$

             = $\frac{\sqrt{3}-1 }{2\sqrt{2} }$

Therefore,

Sin 120° + Cos 75° =  $\frac{\sqrt{3} }{2}$ +  $\frac{\sqrt{3}-1 }{2\sqrt{2} }$

                              = $\frac{\sqrt{6}+\sqrt{3}-1 }{2\sqrt{2} }$

                              = $\frac{2\sqrt{3}+\sqrt{6}-\sqrt{2} }{4}$

Hence probably the question is wrong

Please do recheck the question again

HOPE IT HELPS !!