Question

[Uyên Ngọc]

\(\sqrt{sin^2\left(1+cotx\right)+cos^2\left(1+tanx\right)}\)

Answer 1

[Đỗ Thanh Hải]

= \(\sqrt{sin^2x+sin^2xcotx+cos^2x+cos^2xtanx}\)

= \(\sqrt{sin^2x+sin^2x.\dfrac{cosx}{sinx}+cos^2x+cos^2x.\dfrac{sinx}{cosx}}\)

\(=\sqrt{sin^2x+sinxcosx+cos^2x+sinxcosx}\)

= \(\sqrt{sin^2x+2sinxcosx+cos^2x}\)

= \(\sqrt{\left(sinx+cosx\right)^2}\)