Question

Докажите тождество. 100б

Answer 1

$dfrac{1}{sina-cosa}=dfrac{sina+cosa}{(sina-cosa)(sina+cosa)}=dfrac{sina+cosa}{sin^2a-cos^2a}=\\\=dfrac{sina+cosa}{(sin^2a-cos^2a)cdot 1}=dfrac{sina+cosa}{(sin^2a-cos^2a)(sin^2a+cos^2a)}=dfrac{sina+cosa}{sin^4a-cos^4a}; ;\\\dfrac{sina+cosa}{sin^4a-cos^4a}=dfrac{sina+cosa}{sin^4a-cos^4a}\\\\P.S.; ; ; ; 1=sin^2a+cos^2a\\(a-b)(a+b)=a^2-b^2; ; ; Rightarrow ; ; ; (a^2-b^2)(a^2+b^2)=a^4-b^4$