Question

Evaluate using exact values 1-cos45/1+cos45

Answer 1

Knowing that cos(45°) = 1/√2 is the way forward.


`(1-(1)/(√(2)) )/(1+(1)/(√(2))) = (√(2)-1)/(√(2)+1) = 3 - 2√(2)`

The last step in the equation may not be obious, but the trick here is to multiple numerator and denominator with (1-√2), then the denominator has the special product (a+b)(a-b) = a²-b².