Question

Solve the following equation algebraically:
sin²x - √2cosx = cos²x + √2cosx + 2

Answer 1

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Answer 2

cos x=t
cos^2x =t^2
sin^2x=1-cos^2x=1-t^2
1-t^2-sqrt(2)t=t^2+sqrt(2)t+2
2t^2+2sqrt(2) t-1=0

Answer 3

\[t=(-2\sqrt{2}\pm \sqrt{8+8})/4\]

Answer 4

\[t= (-2\sqrt{2}\pm4)/4\]

Answer 5

\[x=\cos ^{-1}[(-2\sqrt{2}\pm 4)/4]\]