Question

Find the value of the following:

`(cos 70^circ)/(sin 20^circ) + (cos 59^circ)/(sin31^circ) + cos theta/(sin(90^circ - theta))- 8cos^2 60^circ`

Answer 1

cos 60° = `1/sqrt(2)`

`(cos 70^circ)/(sin 20^circ) = (cos(90^circ - 20^circ))/(sin 20^circ) = (sin 20^circ)/(sin 20^circ)` = 1

`(cos 59^circ)/(sin 31^circ) = (cos(90^circ - 31^circ))/(sin 31^circ) = (sin 31^circ)/(sin 31^circ)` = 1

`(cos theta)/(sin(90^circ - theta)) = cos theta/cos theta` = 1

`(cos 70^circ)/(sin 20^circ) + (cos 59^circ)/(sin31^circ) + cos theta/(sin(90^circ - theta))- 8cos^2 60^circ`

= `1 + 1 + 1 - 8(1/2)^2`

= `3 - 8 xx 1/4`

= 3 – 2

= 1