Question

Sin 120°.cos 30°- cos120°.sin 30°

Answer 1

Sin 120° = sin(1×90°+30°)

= sin 30° = 1/2

cos 30° = 1/2√3

cos 120° = cos(1×90°+30°)

= cos 30° = -1/2√3

sin 30° = 1/2

=1/2•1/2√3 + (-1/2√3)•1/2

=1/4√3 + (-1/4√3)

=1/4√3 - 1/4√3

=0

Hope it helps...☺

Answer 2

sin 120° cos 30° - cos 120° sin 30° = 1

Given :

sin 120° cos 30° - cos 120° sin 30°

To find :

The value of the expression

Formula :

sin ( A - B ) = sin A cos B - cos A sin B

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

sin 120° cos 30° - cos 120° sin 30°

Step 2 of 2 :

Find the value of the expression

We use the formula

sin ( A - B ) = sin A cos B - cos A sin B

Thus we get

sin 120° cos 30° - cos 120° sin 30°

= sin ( 120° - 30° )

= sin 90°

= 1

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