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Question:- Prove that sin²72°-sin²60°= √5-1/8

Answer :-

➡We know that , L.H.S= sin²72°-sin²60°

➡ So , L.H.S = cos²18° - sin²60° [ sin²72° = cos²18° ]

➡L.H.S = $( \frac{ \sqrt{10 + 2 \sqrt{5} } }{4} ) ^{2} - ( \frac{ \sqrt{3} }{2} )^{2}$

➡$\frac{10 + 2\sqrt{5} }{16} - \frac{3}{4}$

➡$\frac{2 \sqrt{5} - 2 }{16}$

➡$\frac{ \sqrt{5} - 1 }{8}$ = R.H.S

♦♦HENCE , sin²72°-sin²60°= √5-1/8♦♦

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