Question

解方程:sin^2x+2sinxcosx-3cos^3x=-2

Answer 1

移项

sin^2x+2sinxcosx-3cos^2x+2=0

sin^2x+2sinxcosx-3cos^2x+2(sin^2x+cos^2x)=0

3sin^2x+2sinxcosx-cos^2x=0

(3sinx-cosx)(sinx+cosx)=0

解得sinx=cosx/3

或者x=-cosx

x=kπ+arctan(1/3)

或者

x=kπ-π/4

k∈Z

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