What is the value of sin(135)+cos(225)+tan(315) ?

The value of sin(135)+cos(225)+tan(315) is -1

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sin(135)+cos(225)+tan(315)

sin (13 5^{\circ}) + cos (22 5^{\circ}) + tan (31 5^{\circ})

- 1

Solution steps

sin (13 5^{\circ}) + cos (22 5^{\circ}) + tan (31 5^{\circ})

Use the following trivial identity:

sin (13 5^{\circ}) = \frac{2}{2}

Rewrite using trig identities:

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

Rewrite using trig identities:

tan (31 5^{\circ}) = - 1

= \frac{2}{2} - \frac{2}{2} - 1

Simplify

= - 1

9 sin (\frac{5 π}{4}) + 9 cos (\frac{5 π}{4})

arcsin (sin (\frac{π}{10}))

sin^{2} (\frac{π}{6}) + cos^{2} (\frac{π}{6})

3 \cdot tan (3 0^{\circ})

\frac{1}{sec ^{2} ( 0 )}

What is the value of sin(135)+cos(225)+tan(315) ?
The value of sin(135)+cos(225)+tan(315) is -1