Question

evaluate sin 60.cos 30+sin 30 .cos 60 what is the value of sin (60+30).what can you conclude?

Answer 1

1 as 60+30 =90

so simple it is

Answer 2

Answer:

We know that,

⇒ sin 60° = √3/2

⇒ cos 30° = √3/2

⇒ sin 30° = 1/2

⇒ cos 30° = 1/2

= (sin 60°) + (cos 30°) = √3/2

∴ Substituting/Putting all the values,

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

= $\frac{\sqrt{3} .\sqrt{3} }{2.2} - \frac{1}{2.2}$ (Here . refers to 'x' [multiply])

= $\frac{3}{4} +\frac{1}{4} = \frac{3+1}{4}$ = $\frac{4}{4}$ ⇒ 1

Hence,

We can conclude that

sin 60° cos 30° + sin 30° cos 60° = 1