Question

(cos^2a-sin^2a)/(sin^4a-cos^4a)

Answer 1

$\frac{Cos^{2}\alpha-Sin^{2}\alpha}{Sin^{4}\alpha-Cos^{4}\alpha}=\frac{Cos2\alpha }{(Sin^{2}\alpha-Cos^{2}\alpha)(Sin^{2}\alpha+Cos^{2}\alpha)}=\frac{Cos2\alpha}{-Cos2\alpha*1}=-1\\\\Otvet:\boxed{-1}$

Answer 2

Надеюсь,все понятно

Я в решении использовала тригонометрические формулы

sin^2a+cos^2a=1

cos2a=cos^2a-sin^2a

Answer 3

To simplify the expression (cos^2a - sin^2a)/(sin^4a - cos^4a), we can use the trigonometric identity cos^2a - sin^2a = cos(2a) and sin^4a - cos^4a = -cos(2a).

Replacing the trigonometric identities, the expression becomes:

cos(2a)/(-cos(2a))

Since the numerator and denominator have a common factor of cos(2a), we can cancel them out:

cos(2a) / (-cos(2a)) = -1

Therefore, the simplified form of the expression is -1.