What is the value of 2-2cos((3pi)/2) ?

The value of 2-2cos((3pi)/2) is 2

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2-2cos((3pi)/2)

2 - 2 cos (\frac{3 π}{2})

2

Solution steps

2 - 2 cos (\frac{3 π}{2})

Rewrite using trig identities:

cos (\frac{3 π}{2}) = cos^{2} (\frac{3 π}{4}) - sin^{2} (\frac{3 π}{4})

= 2 - 2 (cos^{2} (\frac{3 π}{4}) - sin^{2} (\frac{3 π}{4}))

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

= 2 - 2 (- \frac{2}{2})^{2} - (\frac{2}{2})^{2}

Simplify

2 - 2 (- \frac{2}{2})^{2} - (\frac{2}{2})^{2} : 2

= 2

2.5 \cdot sin (3 0^{\circ})

tan^{2} (2 (10)) + 1

sin (- 3 7^{\circ})

\frac{cos ( arcsin ( \frac{1}{2} ) )}{tan ( arccos ( - \frac{1}{2} ) )}

\frac{π}{3} - sin (\frac{π}{3})