Question

Prove that cos 20° . cos 40° - sin 5° . sin 25° = $\frac{\sqrt{3} + 1}{4}$.

Answer 1

Answer:

(√3 +1) /4

Step-by-step explanation:

Formula used:

cosA cosB = 1/2 [cos(A+B) +cos(A-B)]

sinA sinB = 1/2 [cos(A-B) - cos(A+B)]

cos 20° . cos 40° - sin 5° . sin 25°

= 1/2 [ cos(20+40) + cos(20-40)]

+1/2 [ cos(5 -25) - cos (5 + 25)]

= 1/2 [ cos60 + cos(-20)]

- 1/2 [ cos(-20) - cos (30)]

= ( 1/2 ) cos60 +(1/2) cos20

- (1/2) cos20 + (1/2)cos (30)

=( 1/2 ) (1/2) +(1/2) cos20- (1/2 )cos20

+ (1/2)(√3/2)

=( 1/2 ) (1/2) + (1/2)(√3/2)

=( 1/4) + (√3/4)

= (√3 +1) /4

I hope this answer helps you