Let `P(x)=((1-cos2x+sin2x)/(1+cos2x+s in2x))^2+((1+cotx+cot^2x)/(1+tanx+tan^2x)),` then the minimum value of `P(x)` equal 1 (b) 2 (c) 4 (d) 16

Options

A. 1
B. 2
C. 4
D. 16

Answer

B

Explanation

`p(x)=((1-cos2x+sin2x)/(1+cos2x+sin2x))^(2)+((1+cotx+cot^(2)x))/(1+tanx+tan^(2)x))`
`=((2sin^(2)x+2sin x cos x)/(2cos^(2)x+2sinx cos x))^(2)+((1)/(tan^(2)x).(tan^(2)x+tanx+1)/(1+tanx+tan^(2)x))`
`=tan^(2)x+cot^(2)x`
`=(tanx-cotx)^(2)+2`