Question

докажите тождество
спасибо)

Answer 1

Ответ:

$\Big(tg\dfrac{9\pi}{4}+tg\Big(\dfrac{5\pi }{2}-a\Big)\Big)^2+\Big(ctg\dfrac{5\pi}{4}+ctg\Big(\pi -a\Big)\Big)^2=\\\\\\=\Big(tg\dfrac{\pi}{4}+ctga\Big)^2+\Big(ctg\dfrac{\pi}{4}-ctga\Big)^2=1+2ctga+ctg^2a+1-2ctga+ctg^2a=\\\\=2+2ctg^2a=2\cdot (1+ctg^2a)=2\cdot \dfrac{1}{sin^2a}=\dfrac{2}{sin^2a}\\\\\\\dfrac{2}{sin^2a}=\dfrac{2}{sin^2a}$

Answer 2

(tg(9π/4)+tg(5π/2-α))²+(ctg5π/4)+ctg(π-α))²=(tg(π/4)+tg(π/2-α))²+

(ctgπ/4-ctgα)²=1+2ctgα+ctg²α+1-2ctgα+ctg²α=2+2ctg²α=

2*(1+ctg²α)=2/sin²α