What is the value of sin(150)+cos(240)-tan(315) ?

The value of sin(150)+cos(240)-tan(315) is 1

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sin(150)+cos(240)-tan(315)

sin (15 0^{\circ}) + cos (24 0^{\circ}) - tan (31 5^{\circ})

1

Solution steps

sin (15 0^{\circ}) + cos (24 0^{\circ}) - tan (31 5^{\circ})

tan (31 5^{\circ}) = tan (13 5^{\circ})

= sin (15 0^{\circ}) + cos (24 0^{\circ}) - tan (13 5^{\circ})

Rewrite using trig identities:

cos (24 0^{\circ}) = 1 - 2 sin^{2} (12 0^{\circ})

= sin (15 0^{\circ}) + 1 - 2 sin^{2} (12 0^{\circ}) - tan (13 5^{\circ})

Use the following trivial identity:

sin (15 0^{\circ}) = \frac{1}{2}

Use the following trivial identity:

sin (12 0^{\circ}) = \frac{3}{2}

Rewrite using trig identities:

tan (13 5^{\circ}) = - 1

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

Simplify

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

= 1

arctan (\frac{7.9253}{22.356 - 12.184 - 7.061})

arccos (\frac{775}{2500})

cos (- \frac{π}{4}) + sin (- \frac{π}{4})

arctan (2) (\frac{6}{8})

0.625 - cos (0.625)

What is the value of sin(150)+cos(240)-tan(315) ?
The value of sin(150)+cos(240)-tan(315) is 1