Trignometry

$cos A = 1 - cos^2 A \Rightarrow cos A = sin^2 A$ $sin^2 A + sin^4 A = cos A + cos^2 A = 1$

since,sin2A+cos2A=1 therefore: cos2A=I-sin2A PUTTING IT IN THE EQUATION GIVEN WE GET; cosA +1-sin2A=1 cosA-sin2A=0 therefore, cosA=sin2A hence, sin2A + sin4A = 1

cos A + cos² A = 1

and...

[cos² A + sin² A = 1]

cos A + cos² A = cos² A + sin² A

so...

cos A = sin² A

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sin² A + sin^{4} A = x

cos A + (cos)² A = x

x = 1

There is a missing + sign between powers of sin.