Question

Without using trigonometric tables , evaluate the following :
`(cot(90^(@)-theta)*sin(90^(@)-theta))/(sintheta)+(cot40^(@))/(tan50^(@))-(cos^(2)20+cos^(2)70^(@))`

Answer 1

`(cot(90^(@)-theta)*sin(90^(@)-theta))/(sintheta)+(cot40^(@))/(tan50^(@))-(cos^(2)20^(@)+cos^(2)70^(@))`
`=(tan*costheta)/(sintheta)+(cot(90^(@)-50^(@)))/(tan50^(@))-{cos^(2)(90^(@)-70^(@))+cos^(2)70^(@)}`
`=(sintheta*costheta)/(costheta*sintheta)+(tan50^(@))/(tan50^(@))-(sin^(2)70^(@)+cos^(2)70^(@))`
`=1+1-1=1`