Prove that cosa.cos2a.cos3a.cos4a=1/16 ,when a=π/9.

Prove that cosa.cos2a.cos3a.cos4a=1/16 ,when a=π/9.

Grade:12th pass

2 Answers

ravi panchal
24 Points
6 years ago
Cos a.cos 2a .cos 4a. Cos 3a Now cos 3a is 1by2 Now we have Cos a.cos 2a .cos 4a. (1/2)Multiply not devide by 2sina Now we have Sin2acos2acos4a/4sinaNow Multiply by 2 and devide by 2Now we have sin4acos4a/8sinaAgain do same We have sin8a /16sinaPut the value of a sin8a equals to sin a so we get 1/16Hence proved
Sai Lokesh
13 Points
3 years ago
Here cos 3a=pi/3 so cos 3a=1/2.
1/2(cos a.cos 2a.cos 4a)
here cos a cos 2a cos 4a are in geometric progression.
formula is sine 2^n a/2^n sine a
so 1/2(sine 8pi/9 / 8 sine pi/9)
1/2(sine pi/9 / 8 sine pi/9)
1/2*1/8 = 1/16.

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