Question

prove that sin70-cos40/cos50-sin20=1/√3​

Answer 1

Solution :

(sin 70° + cos 40°)/(cos 70° + sin 40°)

= [sin 70° + cos(90° – 50°)]/ [cos(90° – 20°) + sin 40°]

= [sin 70° + sin 50°]/ [sin 20° + sin 40°]

Using the formula sin x + sin y = 2 sin(x + y)/2 cos(x – y)/2,

= [2 sin(70° + 50°)/2 cos(70° – 50°)/2] [2 sin(20° + 40°)/2 cos(20° – 40°)/2]

= [sin 60° cos 10°]/ [sin 30° cos(-10°)]

= sin 60°/sin 30°

= (√3/2)/ (1/2)

= √3