prove that
sin 60 + sin 40 - sin 20 = 4 cos sin 20 cos 30
Answers
Answered by
3
Answer:
Consider L.H.S
sin 20 × sin 40 × sin60 × sin80
Step-by-step explanation:
sin 0° = √(0/4) = 0
sin 30° = √(1/4) = ½
sin 45° = √(2/4) = 1/√2
sin 60° = √3/4 = √3/2
sin 90° = √(4/4) = 1
L.H.S = sin60 [ sin20 × sin40 × sin80 ]
L.H.S = √3/2[ sin20 × sin(60 – 20) × sin(60 + 20)]
L.H.S = √3/2[sin 3(20)/4]
L.H.S = √3/2[sin 60/4]
L.H.S = √3/2[√3/2 × 4]
L.H.S = √3/2 × √3/8
L.H.S = 3/16
∴ L.H.S = R.H.S
Similar questions