What is the value of cos(75)+cos(15) ?

The value of cos(75)+cos(15) is sqrt(3/2)

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cos(75)+cos(15)

cos (7 5^{\circ}) + cos (1 5^{\circ})

\frac{3}{2}

Solution steps

cos (7 5^{\circ}) + cos (1 5^{\circ})

Rewrite using trig identities:

2 cos (4 5^{\circ}) cos (3 0^{\circ})

= 2 cos (4 5^{\circ}) cos (3 0^{\circ})

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

Use the following trivial identity:

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

= 2 \cdot \frac{2}{2} \cdot \frac{3}{2}

Simplify

2 \cdot \frac{2}{2} \cdot \frac{3}{2} : \frac{3}{2}

= \frac{3}{2}

tan (arcsin (\frac{1}{3}))

\frac{sin ( 0.1 )}{0.1}

cos (7 4^{\circ})

arctan (\frac{7}{3})

arctan (\frac{7}{5})

What is the value of cos(75)+cos(15) ?
The value of cos(75)+cos(15) is sqrt(3/2)