What is the value of 2sin^2(pi/2)-sin(pi/2)-1 ?

The value of 2sin^2(pi/2)-sin(pi/2)-1 is 0

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2sin^2(pi/2)-sin(pi/2)-1

2 sin^{2} (\frac{π}{2}) - sin (\frac{π}{2}) - 1

0

Solution steps

2 sin^{2} (\frac{π}{2}) - sin (\frac{π}{2}) - 1

Use the following trivial identity:

sin (\frac{π}{2}) = 1

sin (\frac{π}{2})

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}

= 1

= 2 \cdot 1^{2} - 1 - 1

Simplify

= 0

sin (4 5^{\circ}) \cdot cos (4 5^{\circ})

\frac{1}{cos ( 1 )}

cosh (\frac{π}{4} i)

cos (\frac{7}{4} π)

arctan (\frac{3}{10})

What is the value of 2sin^2(pi/2)-sin(pi/2)-1 ?
The value of 2sin^2(pi/2)-sin(pi/2)-1 is 0