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if (4cos^2(9)-3)(4cos^2(27)-3)=tan K then K is equal to

if (4cos^2(9)-3)(4cos^2(27)-3)=tan K then K is equal to

Grade:12th pass

1 Answers

Arun
25750 Points
6 years ago
consider LHS, 

[4 cos^2(9)-3][4 cos^2(27)-3] 

multiplying and dividing with cos9.cos27, 

we get, 

[4cos^3(9)-3cos9][4cos^3(27)-3cos27]/c... 

{but cos3A=4cos^3(A)-3cos(A)} 

==>cos27.cos81/cos9.cos27 

=cos81/cos9 

=sin9/cos9 

=tan9 
 
Hence k = 9°

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