Question

What is `arcsin( sin( -pi/5)) + arctan (tan((2pi)/(7))) -arccos (cos((4pi)/5))`?

Answer 1

`arcsin(sin(-pi/5))+arctan(tan((2pi)/7))-arccos(cos((4pi)/5))=-(5pi)/7`

Explanation:

As `arcsin(sina)=a`, `arctan(tanb)=b` and `arccos(cosc)=c`

`arcsin(sin(-pi/5))+arctan(tan((2pi)/7))-arccos(cos((4pi)/5))`

= `-pi/5+(2pi)/7-(4pi)/5`

= `+(2pi)/7-(5pi)/5`

= `+(2pi)/7-pi`

= `-(5pi)/7`