Question

SHOW that sin600.cos330 +cos120.sin150=1

Answer 1

sin 600 . cos 330 + cos 120 . sin 150 = 1
sin (1 × 360 + 240) . cos (360 - 30) + cos (180 - 60) . sin (180 - 30) = 1
sin 240 . cos 30 + (-cos 60) . sin 30 = 1
sin (180 + 60) . 1/2√3 - 1/2 . 1/2 = 1
-sin 60 . 1/2√3 - 1/4 = 1
-1/2√3 . 1/2√3 - 1/4 = 1
-3/4 - 1/4 = 1
-4/4 = 1
-1 ≠ 1

Answer 2

Answer:

$\sin 600\times \cos330+\cos 120\times \sin 150=-1$

Step-by-step explanation:

To show : $\sin 600\times \cos330+\cos 120\times \sin 150=-1$

Solution :

Take LHS,

$\sin 600\times \cos330+\cos 120\times \sin 150$

Applying trigonometry,

$\sin 600=\sin(3\times 180+60)=-\sin(60)$

$\cos 330=\cos(360-30)=\cos(30)$

$\cos 120=\cos(180-60)=-\cos(60)$

$\sin 150=\sin(180-30)=\sin(30)$

Substitute the values in the expression,

$=-\sin(60)\times \cos(30)-\cos(60)\times \sin(30)$

Put all the values,

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

$=-\frac{3}{4}-\frac{1}{4}$

$=\frac{-3-1}{4}$

$=\frac{-4}{4}$

$=-1$

=RHS

Therefore, $\sin 600\times \cos330+\cos 120\times \sin 150=-1$