What is the value of cos^2(pi/4)-sin((7pi)/6) ?

The value of cos^2(pi/4)-sin((7pi)/6) is 1

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cos^2(pi/4)-sin((7pi)/6)

cos^{2} (\frac{π}{4}) - sin (\frac{7 π}{6})

1

Solution steps

cos^{2} (\frac{π}{4}) - sin (\frac{7 π}{6})

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Rewrite using trig identities:

sin (\frac{7 π}{6}) = - \frac{1}{2}

= (\frac{2}{2})^{2} - (- \frac{1}{2})

Simplify

(\frac{2}{2})^{2} - (- \frac{1}{2}) : 1

= 1

cot^{2} (6 0^{\circ})

arctan (\frac{34}{39})

arcsin (cos (- \frac{3 π}{4}))

arctan (\frac{- 5}{5 3})

arccos (\frac{5}{51})

What is the value of cos^2(pi/4)-sin((7pi)/6) ?
The value of cos^2(pi/4)-sin((7pi)/6) is 1