Question

Докажите тождество. 100б

Answer 1

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