Question

Найти 1-sin²α/1+sin2α ,если tgα=-5

Answer 1

$\frac{1-sin^2\alpha} {1-sin2\alpha} =\frac{cos^2\alpha} {1-2sin\alpha cos\alpha }=\frac{cos^2\alpha} {sin^2 \alpha + cos^2 \alpha - 2 sin \alpha cos \alpha }= \frac{cos^2\alpha} {(sin\alpha-cos\alpha)^2 }=$

$= \frac{ \frac{cos^2 \alpha }{cos^2 \alpha }}{( \frac{sin \alpha }{cos \alpha }- \frac{cos \alpha }{cos \alpha })^2 }= \frac{1}{(tg \alpha- 1)^2 } =\frac{1}{(-5- 1)^2 }=\frac{1}{36 }$