What is the value of 2sin(36)cos(36) ?

The value of 2sin(36)cos(36) is (sqrt(2)(1+sqrt(5))sqrt(5-\sqrt{5)})/8

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2sin(36)cos(36)

2 sin (3 6^{\circ}) cos (3 6^{\circ})

\frac{2 ( 1 + 5 ) 5 - 5}{8}

Solution steps

2 sin (3 6^{\circ}) cos (3 6^{\circ})

Rewrite using trig identities:

sin (3 6^{\circ}) = \frac{2 5 - 5}{4}

Rewrite using trig identities:

cos (3 6^{\circ}) = \frac{5 + 1}{4}

= 2 \cdot \frac{2 5 - 5}{4} \cdot \frac{5 + 1}{4}

Simplify

2 \cdot \frac{2 5 - 5}{4} \cdot \frac{5 + 1}{4} : \frac{2 ( 1 + 5 ) 5 - 5}{8}

= \frac{2 ( 1 + 5 ) 5 - 5}{8}

tan^{2} (24 0^{\circ}) + sec^{2} (22 5^{\circ})

70 cos (3 0^{\circ})

1 + 2 cos (\frac{π}{3})

arctan (56)

sin (\frac{π}{4}) \cdot sin (\frac{π}{4})

What is the value of 2sin(36)cos(36) ?
The value of 2sin(36)cos(36) is (sqrt(2)(1+sqrt(5))sqrt(5-\sqrt{5)})/8