Question

sin π\3+tan π\6+sin π\2×cos π\3​

Answer 1

$\frac{5+\sqrt{3} }{2\sqrt{3} }$

Step-by-step explanation:

Given,

          ∵π=180°

    So,

         $sin\frac{\pi}{3} +tan\frac{\pi}{6} +sin\frac{\pi}{2}$×$cos\frac{\pi}{3}$

       =$sin\frac{180^\circ}{3}+tan\frac{180^\circ}{6} +sin\frac{180^\circ}{2}$×$cos\frac{180^\circ}{3}$       [∴put the value of π]

       

       =$sin60^\circ+tan30^\circ+sin90^\circ$×$cos60^\circ$

       =$\frac{\sqrt{3} }{2} +\frac{1}{\sqrt{3} } +1$×$\frac{1}{2}$

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

       =$\frac{3+2+\sqrt{3} }{2\sqrt{3} }$

       =$\frac{5+\sqrt{3} }{2\sqrt{3} }$

     

The solution is $\frac{5+\sqrt{3} }{2\sqrt{3} }$