What is the value of sec(pi-pi/3)-csc(-45)sin((5pi)/4) ?

The value of sec(pi-pi/3)-csc(-45)sin((5pi)/4) is -3

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sec(pi-pi/3)-csc(-45)sin((5pi)/4)

sec (π - \frac{π}{3}) - csc (- 4 5^{\circ}) sin (\frac{5 π}{4})

- 3

Solution steps

sec (18 0^{\circ} - 6 0^{\circ}) - csc (- 4 5^{\circ}) sin (22 5^{\circ})

Simplify

= sec (12 0^{\circ}) - csc (- 4 5^{\circ}) sin (22 5^{\circ})

Use the following property:

csc (- x) = - csc (x)

csc (- 4 5^{\circ}) = - csc (4 5^{\circ})

= sec (12 0^{\circ}) - (- csc (4 5^{\circ})) sin (22 5^{\circ})

Simplify

= sec (12 0^{\circ}) + csc (4 5^{\circ}) sin (22 5^{\circ})

Use the following trivial identity:

sec (12 0^{\circ}) = - 2

Use the following trivial identity:

csc (4 5^{\circ}) = 2

Rewrite using trig identities:

sin (22 5^{\circ}) = - \frac{2}{2}

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

Simplify

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

= - 3

\frac{sin ( 6 0 ^{\circ} )}{sin ( 4 0 ^{\circ} )}

2.4 \cdot cos (3 0^{\circ})

cot (π + \frac{π}{4})

sin (126.8 7^{\circ})

\frac{2 cos ( \frac{π}{4} ) - sin ( \frac{3 π}{4} )}{1 - cos ( \frac{π}{4} )}

What is the value of sec(pi-pi/3)-csc(-45)sin((5pi)/4) ?
The value of sec(pi-pi/3)-csc(-45)sin((5pi)/4) is -3