Question

prove that cos36°=√5+1/4

Answer 1

Hey !!!

•°• cos36° = cos2 × 18 °

°•° we know that cos2A = 1 - sin²A

similarly ,

=> 1 - 2 ( sin²18° )

but sin18° = (√5 - 1) /4

hence,

=> 1 - 2 {( √5 - 1 )/4 }²

=> 1 - 2 {( 5 + 1 - 2√5 ) /16 }

=> 16 - 2 ( 6 - 2√5 )

=> 16 - 12 + 4√5 / 16

=> 4 + 4√5 / 16

=> 4 ( 1 + √5 )/16

=> 1 + √5 /4

Hence, cos36° = √5 + 1 /4 Answer ✔

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Hope it helps you !!!

@Rajukumar111