Question

prove that , sin 120 × cos 330 + cos 240 × sin 330 = 1​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation:

To Prove :-

sin120° × cos330° + cos240° × sin330° = 1

Formula Required :-

1) sin120° = √3/2

2) cos330° = √3/2

3) cos240°  = -1/2

4) sin330° = -1/2

Solution :-

sin120° = sin(90° + 30°)

= cos30°

= √3/2

cos330° = cos(360° - 30°)

= cos30°

= √3/2

cos240° = cos(270° - 30°)

= -sin(30°)

= -1/2

sin330° = sin(360° - 30°)

= -sin30°

= -1/2

Finding value of L.H.S :-

= sin120° × cos330° + cos240° × sin330°

= (√3/2 × √3/2) + (-1/2 × -1/2)

= 3/4 + 1/4

= 3 + 1/4

= 4/4

= 1

= R.H.S

Hence proved that 'sin 120 × cos 330 + cos 240 × sin 330 = 1​'