Question

已知tanθ=2,求2+sinθcosθ-cosθ^2

Answer 1

2+sinθcosθ-cosθ^2

= (2sinθ^2 + cosθ^2 +sinθcosθ)/1

= (2sinθ^2 + cosθ^2 +sinθcosθ)/(sinθ^2 + cosθ^2)

= (2tanθ^2+1+tanθ)/(tanθ^2+1)

= (2*4+1+2)/(4+1)

=11/5