Question

sin^4alpha-cos^4alpha+1= sin^2alpha

Answer 1

(Sin^4 alpha-cos^4alpha)+1 = sin^2alpha
(sin^2alpha+cos^2alpha)(sin^2alpha-cos^2alpha) = sin^2alpha-1
(sin^2alpha+cos^2alpha)(cos^2alpha-sin^2alpha) = 1-sin^2alpha
"" "" =cos^2alpha
(cos^2alpha-sin^2alpha)= cos^2alpha/(sin^2alpha+cos^2alpha)
"" "" =1/(tan^2alpha+1)
=1/sec^2alpha = cos^2alpha
cos^2alpha-sin^2alpha = cos^2alpha
Sin^2alpha = cos^2alpha-cos^2alpha
=0