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Popular >

(cos(pi)-sec(pi/4)}{cot(pi/6)+sin(\frac{3pi)/2)}

Solution

\frac{cos ( π ) - sec ( \frac{π}{4} )}{cot ( \frac{π}{6} ) + sin ( \frac{3 π}{2} )}

Solution

\frac{( - 1 - 2 ) ( 3 + 1 )}{2}

+1

Solution steps

\frac{cos ( π ) - sec ( \frac{π}{4} )}{cot ( \frac{π}{6} ) + sin ( \frac{3 π}{2} )}

Rewrite using trig identities:

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

= \frac{cos ( π ) - sec ( \frac{π}{4} )}{cot ( \frac{π}{6} ) + 2 sin ( \frac{3 π}{4} ) cos ( \frac{3 π}{4} )}

Use the following trivial identity:

cos (π) = (- 1)

Use the following trivial identity:

sec (\frac{π}{4}) = 2

Use the following trivial identity:

cot (\frac{π}{6}) = 3

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

= \frac{- 1 - 2}{3 + 2 \cdot \frac{2}{2} ( - \frac{2}{2} )}

Simplify

\frac{- 1 - 2}{3 + 2 \cdot \frac{2}{2} ( - \frac{2}{2} )} : \frac{( - 1 - 2 ) ( 3 + 1 )}{2}

= \frac{( - 1 - 2 ) ( 3 + 1 )}{2}

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-12.5sin(53.13)+11.25

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Frequently Asked Questions (FAQ)

What is the value of (cos(pi)-sec(pi/4)}{cot(pi/6)+sin(\frac{3pi)/2)} ?
The value of (cos(pi)-sec(pi/4)}{cot(pi/6)+sin(\frac{3pi)/2)} is ((-1-sqrt(2))(sqrt(3)+1))/2