What does cos(arctan(pi/2))-sin(arc cot(pi/4)) equal?

1 Answer
Jun 8, 2016

cos (arc tan (frac{pi }{2}))-sin (arc cot (frac{pi }{4}))=frac{2}{sqrt{pi ^2+4}}-frac{4}{sqrt{pi ^2+16}}

Explanation:

cos (arctan (frac{pi }{2}))-sin (arc cot (frac{pi }{4}))
We know,
cos (arctan (frac{pi }{2}))
using the following identity,
cos (arctan (x))=frac{1}{sqrt{1+x^2}}
=frac{1}{sqrt{1+(frac{pi }{2})^2}}
Refining it,
=\frac{2}{\sqrt{4+\pi ^2}}

Also,
sin (arc cot (frac{pi }{4}))
using the following identity,
sin (arc cot (x))=frac{1}{sqrt{1+x^2}}
sin (arc cot (x))=frac{1}{sqrt{1+x^2}}
Refining it,
=frac{4}{sqrt{16+pi ^2}}

Finally,
=frac{2}{sqrt{pi ^2+4}}-frac{4}{sqrt{pi ^2+16}}