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

Options

A. `0`
B. `1`
C. `-1`
D. none of these

Answer

B

Explanation

Given expression`=(tan theta*costheta)/(sintheta)+(cot40^(@))/(tan(90^(@)-40^(@)))-{cos^(2)20^(@)+cos^(2)(90^(@)-20^(@))}`
`=(sintheta)/(costheta)*(costheta)/(sintheta)+(cot40^(@))/(cot40^(@))-{cos^(2)20^(@)+sin^(2)20^(@)}=1+1-1=1.`