cos^2 72º – sin^2 54° =
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Step-by-step explanation:
cos²72 = cos²(90 - 18) = sin²18 = (√5 - 1)/4
sin²54 = sin²(90 - 36) = cos²36 = (√5 + 1)/4
now, cos²72 - sin²54
\bold{\implies \{\frac{\sqrt{5} - 1}{4}\}^2 - \{\frac{\sqrt{5} + 1}{4}\}^2 }⟹{
4
5
−1
}
2
−{
4
5
+1
}
2
\bold{\implies \frac{1}{16} [(\sqrt{5} - 1)^2 - (\sqrt{5} + 1)^2]}⟹
16
1
[(
5
−1)
2
−(
5
+1)
2
]
\bold{\implies \frac{1}{16}[\{\sqrt{5} - 1 - \sqrt{5} - 1\}\{\sqrt{5} - 1 + \sqrt{5} + 1\}]}⟹
16
1
[{
5
−1−
5
−1}{
5
−1+
5
+1}]
\bold{\implies \frac{1}{16}[\{-2*(2\sqrt{5})\}]}⟹
16
1
[{−2∗(2
5
)}]
\bold{\implies \frac{-\sqrt{5}}{4}}⟹
4
−
5
I HOPE IT'S HELP YOU
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