Question

7cos^(2)a - 5sin^(2)a

Answer 1

Ответ:

$7cos^2a-5sin^2a=5\, (cos^2a-sin^2a)+2cos^2a=5\, cos2a+2\cdot \dfrac{1+cos2a}{2}=\\\\=5cos2a+1+cos2a=6cos2a+1$

$-1\leq cos2a\leq 1\\\\-6\leq 6cos2a\leq 6\\\\-5\leq 6cos2a+1\leq 7$