Question

If sinx+sin²x=1,then cos²x+cosx=

Answer 1

Answer:

tan(x) × sec(x)

Step-by-step explanation:

sin x + sin^2 x=1

√(1-cos^2 x)+1-cos^2 x=1

√(1-cos^2 x)-cos^2 x=0

√(1-cos^2 x)=cos^2 x

1-cos^2 x=cos^4 x

1=cos^4 x +cos^2 x

1=cos^2 x (1+cos^2 x)

1/cos^2 x = 1+cos^2 x

sec^2 x=1+cos^2 x

sec^2 x -1 =cos^2 x

-tan^2 x=cos^2 x..........since 1-tan^2 x=sec^2 x

cos x = √(-tan^2 x)

= itanx where i = √(-1)

therefore

cos^2 x + cos x

=-tan^2 x+ i tan x

=i tan x - tan^2 x