Question

Prove that,
(4cos^2 9-3)(4cos^2 27-3)=tan9

Answer 1

$\huge {\underline {\underline {\mathtt {\purple {Answer\: :-}}}}}$

⇛To Prove:- (4cos^2 9-3)(4cos^2 27-3)=tan9

$\huge {\underline {\underline {\mathbb {\orange {Consider LHS, }}}}}$

$\text {⇒ [4 cos^2(9)-3][4 cos^2(27)-3]}$

⇛Multiplying and dividing with cos9.cos27,

$\huge {\underline {\underline {\mathbb {\pink {⇛we get, }}}}}$

$\text {⇒[4cos^3(9)-3cos9][4cos^3(27)-3cos27]/cos9.cos27}$

$\text {⇒{but cos3A=4cos^3(A)-3cos(A)}}$

$\text {⇒cos27.cos81/cos9.cos27}$

$\text {⇒cos81/cos9}$

$\text {⇒sin9/cos9}$

$\text {⇒tan9}$

$\huge {\underline {\underline {\mathbb {\blue {⇛LHS=RHS}}}}}$

$<font color ="red">$

$<marquee Scrollamount =30> Hence proved... </marquee >$

Answer 2

I Hope above given attachment HElPFUL to YoU..