Question

please Sol the question fast

Answer 1

Sin 54° = Cos 36° = ( 1/4 ) (√5 + 1) 

=> Cos 54° = √( 1 - Sin² 54°) = ( 1/4 ) √[ 10 – 2 √5 ] 

=> 1 – 2 Sin² 27° = ( 1/4 ) √[ 10 – 2 √5 ] 

=> 2 Sin² 27° = 1/2 [ 1 - ( 1/4 ) √[ 10 – 2 √5 ] 

Multiply both the sides by 8 – 

=> 16 Sin² 27° = 8 - 2 √[ 10 – 2 √5 ] = [√ ( 5 + √5 ) - √ ( 3 - √5 ) ] ² 

=> 4 Sin 27° = √( 5 + √5 ) - √( 3 - √5 ) ......... Proved 

(Neglecting – ve value as Sin is + ve.) 

Hope it's help you