Question

Proove that :

sin²72° - sin²60° = √5-1/8

Answer 1

$\boxed{Question-}$Proove that :

sin²72° - sin²60° = √5-1/8

$\huge\boxed{Solution}$

We have ,

LHS = sin²72° - sin² 60°

LHS = cos²18° - sin² 60°............[sin 72° = cos18°]

LHS =
$( \frac{ \sqrt{10 + 2 \sqrt{5} } }{4}) {}^{2} - ( \frac{ \sqrt{3} }{2}) {}^{2} \\ = \frac{10 + 2 \sqrt{5}}{16} - \frac{3}{4} \\ \\ = \frac{2 \sqrt{5 } - 2}{16} \\ = \frac{\sqrt{5} - 1}{8} =RHS$

Answer 2

Heya mate
The answer of ur question is in the attachment

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