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