Question

find value of sin 120° cos 330° - sin 240° cos 390​°​

Answer 1

Answer:

after changing angles it become

sin60 cos30 -(-sin60) cos30

√3/2×√3/2+√3/2×√3/2

=3/4+3/4=6/4 =3/2

Answer 2

Answer:

Required value of the given expression is 3/2.

Step-by-step explanation:

Given expression is sin 120° cos 330° - sin 240° cos 390°

We can use the trigonometric identities to simplify the given expression.

sin 120° = sin (180° - 60°) = sin 60° = √3/2

cos 330° = cos (360° - 30°) = cos 30° = √3/2

sin 240° = sin (180° + 60°) = - sin 60° = - √3/2

cos 390° = cos (360° + 30°) = cos 30° = √3/2

Now, we can substitute these values in the given expression and simplify:

sin 120° cos 330° - sin 240° cos 390°

= (√3/2)(√3/2) - (- √3/2)(√3/2)

= (3/4) + (3/4)

= 3/2

Therefore, sin 120° cos 330° - sin 240° cos 390° = 3/2.

Some important formulas of Trigonometry,

$sin(x) = \cos(\frac{\pi}{2} - x) \\ \tan(x) = \cot(\frac{\pi}{2} - x) \\ \sec(x) = \csc(\frac{\pi}{2} - x) \\ \cos(x) = \sin(\frac{\pi}{2} - x) \\ \cot(x) = \tan(\frac{\pi}{2} - x) \\ \csc(x) = \sec(\frac{\pi}{2} - x)$

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