Question

Cos²x + sin2x - 1 = 0, 0° ≤ x ≤ 90°, tan x =​

Answer 1

0 and arctan(0.5)

Explanation:

if sin2x=2sinx*cosx and 1=sin²x+cos²x, then

cos²x+2sinxcosx-sin²x-cos²x=0;

2sinxcosx-sin²x=0; (to divide by cos²x)

2tanx-tan²x=0;

`\left[\begin{array}{ccc}tan(x)=0\\ tan(x)=1/2\end{array} \ => \ \left[\begin{array}{ccc}x=pi*n\\x=arctan(1/2)+pi*n\end{array} \ => \ \left[\begin{array}{ccc}x=0\\x=arctan(0,5)\end{array}`