Reescreva # sin ^ 4 (x) tan ^ 2 (x) # em termos do primeiro poder do cosseno?

Responda:

#=> (1-3cos^2(x) +3cos^4(x) -cos^6(x))/cos^2(x)#

Explicação:

#sin^4(x)tan^2(x)#

#=> (1-cos^2(x))^2(sin^2(x))/cos^2(x)#

#=> (1-2cos^2(x) + cos^4(x))(sin^2(x))/cos^2(x)#

#=>( sin^2(x)-2sin^2(x)cos^2(x) + sin^2(x)cos^4(x))/cos^2(x)#

#=> ((1-cos^2(x)) -2(1-cos^2(x))cos^2(x)+(1-cos^2(x))cos^4(x))/cos^2(x)#

#=> (1-cos^2(x) -2cos^2(x)+2cos^4(x)+cos^4(x)-cos^6(x))/cos^2(x)#

#=> (1-3cos^2(x) +3cos^4(x) -cos^6(x))/cos^2(x)#