Question

Evaluate sin60 cos30+sin30 cos60. What is the value of sin(60+30). What can you conclude?

Answer 1

sin 60 = root 3 /2 
cos 30 = root 3 /2 
sin 30 = 1/2 
cos 60 = 1/2 
= (root 3 /2 ) (root 3 / 2) + (1/2) (1/2) 
= 3/4 + 1/4 
= 4/4 
= 1 
sin 60 + 30 = 90 
where sin 90 = 1 

Answer 2

Given:

We have given an equation of trignometric ratios.

To Find:

We have to find the value of sin(60+30)?

Step-by-step explanation:

• Trigonometric ratio:

• Trigonometry is the study of right-angled triangle and where the trigonometry ratio deals with the ratio of side of triangle.

• We have given an equation which is written as the

       $Sin60^\circ Cos30^\circ+Sin30^\circ Cos60^\circ$

       We know the values of trigonometric ratios at different angles

• Some of required values are

       $Sin60^\circ=\frac{\sqrt{3} }{2}\\Cos30^\circ=\frac{\sqrt{3} }{2}\\\\Sin30^\circ=\frac{1 }{2}\\\\Cos60^\circ=\frac{1 }{2}\\\\Sin90^\circ=1$

• Now we put the values which is required in the above equation and after we will get

          $=\frac{\sqrt{3} }{2} \times\frac{\sqrt{3} }{2}+\frac{1}{2}\times \frac{1}{2} \\\\=\frac{3}{4} +\frac{1}{4} \\=\frac{4}{4}=1$

• Hence Sin(60+30) is calculated by the

       $Sin(60^\circ+30^\circ)=Sin90^\circ=1$

Hence we conclude that  $Sin60^\circ Cos30^\circ+Sin30^\circ Cos60^\circ=Sin90^\circ$.