Question

cos^2 72º – sin^2 54° =​

Answer 1

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