Question

Помогите решить ............................

Answer 1

$1)\; \; sin^2a-sin^2\beta =(sina-sin\beta)(sina+sin\beta )=\\\\=2\cdot sin\frac{a-\beta }{2}\cdot cos\frac{a+\beta }{2}\; \cdot \; 2sin\frac{a+\beta }{2}\cdot cos\frac{a-\beta }{2}=sin(a-\beta )\cdot sin(a+\beta )$

$2)\; \; cos^2a-cos^2\beta =(cosa-cos\beta )(cosa+cos\beta )=\\\\=-2sin\frac{a+\beta }{2}\cdot sin\frac{a-\beta }{2}\; \cdot \; 2cos\frac{a+\beta }{2}\cdot cos\frac{a-\beta }{2}=-sin(a+\beta )\cdot sin(a-\beta )$

$3)\; \; \frac{3}{4}-sin^2x=(\frac{\sqrt3}{2})^2-sin^2x=sin^2\frac{\pi}{3}-sin^2x=\\\\=\Big[\; sin^2a-sin^2\beta =sin(a-\beta )\cdot sin(a+\beta )\; \Big]=\\\\=sin(\frac{\pi}{3}-x)\cdot sin(\frac{\pi}{3} +x)$

$4)\; \; cos^2x-\frac{1}{2}=cos^2x-cos^2\frac{\pi}{4}=\\\\=\Big[\; cos^2a-cos^2\beta =-sin(a+\beta )\cdot sin(a-\beta )\; \Big]=\\\\-sin(x+\frac{\pi}{4})\cdot sin(x-\frac{\pi}{4})$