Find the general solution for 4sin^2x+6cos^2x=5

Steps to solve Find the general solution for 4sin^2x+6cos^2x=5

⇒4sin^2x+6cos^2x=5

⇒4sin^2x+6(1-sin^2x)=5

⇒4sin^2x+6-6sin^2x=5

⇒6-2sin^2x=5

⇒-2sin^2x=5-6=-1

⇒2sin^2x=1

⇒sin^2x=1/2

⇒sinx=1/√2

⇒sinx=sin(π/4)

⇒x=nπ+(-1)^n(π/4)

Hence the general solution for 4sin^2x+6cos^2x=5 is nπ+(-1)^n(π/4)

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