What is the value of 2sin(pi/4)2cos(pi/4) ?

The value of 2sin(pi/4)2cos(pi/4) is 2

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2sin(pi/4)2cos(pi/4)

2 sin (\frac{π}{4}) 2 cos (\frac{π}{4})

2

Solution steps

2 sin (\frac{π}{4}) \cdot 2 cos (\frac{π}{4})

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{π}{4})

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

cos (\frac{π}{4})

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

= 2 \cdot \frac{2}{2} \cdot 2 \cdot \frac{2}{2}

Simplify

2 \cdot \frac{2}{2} \cdot 2 \cdot \frac{2}{2} : 2

2 \cdot \frac{2}{2} \cdot 2 \cdot \frac{2}{2}

Multiply fractions:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= \frac{2 2 \cdot 2 \cdot 2}{2 \cdot 2}

Cancel the common factor:

2

= 22

Apply radical rule:

a a = a

22 = 2

= 2

= 2

sin (2.1)

sin (2.6)

sin (16 5^{\circ}) cos (7 5^{\circ})

2 + sin (\frac{3 π}{4})

arcsin (sec (π))

What is the value of 2sin(pi/4)2cos(pi/4) ?
The value of 2sin(pi/4)2cos(pi/4) is 2