Question

$\cos(80) - \cos(40) + \sqrt{3} \cos(70) = 0$

Answer 1

cos 80 - cos 40 + √3cos 70
=-2sin 1/2(80+40) sin 1/2(80-40)+√3cos 70
=-2 sin 60 sin 20+√3cos70
=-2(√3/2)sin 20+√3 cos 70
=-√3sin20+√3cos70
= -√3sin 20 + √3 sin(90-70)
=-√3sin 20+√3sin 20
=0

Answer 2

Step-by-step explanation:

= 2sin 80°+40°/2 sin 40°- 80°/2 + √3 cos70°

= -2sin60°sin20°+√3 cos70°

= -2 ×(√3/2) sin20°+ √3 cos 70°

= - √3 sin20° + √3 cos 70°

= -√3 sin20° + √3 cos(90° - 20°)

= -√ 3 sin20° + √3 sin20°

= 0 = RHS [PROVED]

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We use -

sin60°=√3/2

cosC - cosD = 2sin (C- D/2) sin(D- C/2)