What is the value of cos(arctan(5/7)+arctan(1/6)) ?

The value of cos(arctan(5/7)+arctan(1/6)) is (sqrt(2))/2

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cos(arctan(5/7)+arctan(1/6))

cos (arctan (\frac{5}{7}) + arctan (\frac{1}{6}))

\frac{2}{2}

Solution steps

cos (arctan (\frac{5}{7}) + arctan (\frac{1}{6}))

Rewrite using trig identities:

arctan (\frac{5}{7}) + arctan (\frac{1}{6}) = arctan (1)

= cos (arctan (1))

Rewrite using trig identities:

cos (arctan (1)) = \frac{1 + 1 ^{2}}{1 + 1 ^{2}}

= \frac{1 + 1 ^{2}}{1 + 1 ^{2}}

Simplify

= \frac{2}{2}

arctan (1.75)

\frac{1 - cos ( 15 0 ^{\circ} )}{2}

arctan (\frac{7}{9})

tan (63 0^{\circ})

arctan (\frac{- 4}{4})

What is the value of cos(arctan(5/7)+arctan(1/6)) ?
The value of cos(arctan(5/7)+arctan(1/6)) is (sqrt(2))/2