Question

prove thatcos20-cos40-cos80​

Answer 1

Answer:

Given expression = cos 80° cos20° cos40°

= (1/2) 2cos 80° cos20° cos40°

Use 2 cosAcosB = cos(A+B) + cos(A-B) formula.

= (1/2){ cos (80°+20°) + cos(80°–20°)}cos40°

= (1/2)( cos 100° + cos 60°)cos40°

= (1/2) cos 100° cos 40° + (1/2) cos60°cos40°

= (1/2)(1/2)2cos100°cos40° +(1/2)(1/2)cos40°

= (1/4){cos140° + cos60°}+ (1/4)cos40°

= (1/4)(cos140° + cos40°) + (1/4)cos 60°

= (1/4){cos(180°-40°) + cos 40) +(1/4) (1/2)

But cos (180° -x) = -cos x. So,

= (1/4)(-cos40°+cos40°) + 1/8

= 1/8

here is your answer...

hopes it helps you...

Answer 2

Step-by-step explanation:

• Cos 20° - Cos 40° - Cos 80°
• Cos 20° - ( Cos 40° + Cos 80° )
• Cos 20° - [ 2 Cos ( 40° + 80° ) / 2 ] [ Cos ( 80° - 40° ) / 2 ]
• Cos 20° - 2 Cos 60° Cos 20°
• Cos 20° - 1 - 2 Cos 60°

❤❤❤Cos 60° = ½❤❤❤

• Cos 20° - 1 - 2 ( $\frac{1}{2}$
• Cos 20° ( 0 )
• Cos 20° - Cos 40° - Cos 80° = 0