Question

evaluate sin 60° cos 30° + cos 30 sin 60°​

Answer 1

To evaluate:-

• sin 60° cos 30° + cos 30° sin 60°

Solution:-

$\bigstar \sf \:sin \: 60 \degree\: cos \: 30 \degree + cos \: 30 \degree \: sin \: 60 \degree$

Sin 60° = √3/2

Cos 30° = √3/2

Put the values,

$\implies \sf \dfrac{ \sqrt{3} }{2} \times \dfrac{ \sqrt{3} }{2} + \dfrac{ \sqrt{3} }{2} \times \dfrac{ \sqrt{3} }{2}$

$\implies \sf \dfrac{3}{4} + \dfrac{3}{4}$

$\implies \sf \dfrac{3 + 3}{4}$

$\implies \sf \dfrac{ \cancel{6}}{ \cancel{4}}$

$\implies \sf \dfrac{3}{2}$

Therefore,

$\large \bigstar \sf \:sin \: 60 \degree\: cos \: 30 \degree + cos \: 30 \degree \: sin \: 60 \degree = \dfrac{3}{2}$

Answer 2

Answer:

1

Step-by-step explanation:

Since, sin A = cos ( 90 - A ),

sin 60° . cos 30° + cos 60° . sin 30

= sin 60° . sin ( 90° - 30° ) + cos 60° . cos ( 90° - 30° )

= sin 60° . sin 60° + cos 60° . cos 60°

= sin^2 60° . cos^2 60°

= 1

( as sin^2 A + cos^2 A = 1 )