If `f(theta)=(1-sin2theta+cos2theta)/(2cos2theta)` , then value of `8f(11^0)f(34^0)` is ____

Answer

0.5

Explanation

`f(theta) = (1-sin 2theta + cos 2 theta)/(2 cos 2 theta ) `
`" " = ((cos theta - sin theta )^(2)+ ( cos ^(2) theta - sin^(2) theta))/( 2 ( cos theta - sin theta) (cos theta + sin theta))`
`" " = ( cos theta)/( cos theta + sintheta )`
`" "= (1)/( 1+ tan theta)`
`f (11^(@)) * f( 34^(@)) = (1)/(( 1+ tan 11^(@))) xx (1)/(( 1+ tan 34^(@)))`
`" " = (1)/((1+ tan 11^(@))) xx (1)/( (1 + tan(45^(@) - 11^(@))))`
`" " = (1)/( ( 1+ tan 11^(@))) xx (1)/(1+ (1- tan 11^(@))/(1+ tan 11^(@)))`
`" " = (1)/((1+tan 11^(@))) xx ((1+ tan 11^(@)))/( 2)`
`= (1)/(2)`