What is the value of cos(330)csc(150)-tan(150)sec(210) ?

The value of cos(330)csc(150)-tan(150)sec(210) is sqrt(3)-2/3

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cos(330)csc(150)-tan(150)sec(210)

cos (33 0^{\circ}) csc (15 0^{\circ}) - tan (15 0^{\circ}) sec (21 0^{\circ})

3 - \frac{2}{3}

Solution steps

cos (33 0^{\circ}) csc (15 0^{\circ}) - tan (15 0^{\circ}) sec (21 0^{\circ})

Rewrite using trig identities:

cos (33 0^{\circ}) = \frac{3}{2}

Rewrite using trig identities:

csc (15 0^{\circ}) = 2

Rewrite using trig identities:

tan (15 0^{\circ}) = - \frac{3}{3}

Rewrite using trig identities:

sec (21 0^{\circ}) = - \frac{2 3}{3}

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

Simplify

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

= 3 - \frac{2}{3}

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

sin (2 \frac{3}{5})

sin (75.5 2^{\circ})

cot (99 0^{\circ})

cos (2 π \cdot 3)

What is the value of cos(330)csc(150)-tan(150)sec(210) ?
The value of cos(330)csc(150)-tan(150)sec(210) is sqrt(3)-2/3