Question

[Thư Nguyễn Ngọc Anh]

Rút gọn biểu thức:

\(A=\sin^210+\sin^220+\sin^230+\sin^280+\sin^270+\sin^260\)

\(B=\left(1+\tan^2\alpha\right)\left(1-\sin^2\alpha\right)+\left(1+\cot^2\alpha\right)\left(1-\cos^2\alpha\right)\)

Answer 1

[Nguyễn Tấn An]

\(A=sin^210+sin^220+sin^230+sin^280+sin^270+sin^260=sin^210+sin^220+sin^230+cos^210+cos^220+cos^230=1+1+1=3\)\(B=\left(1+tan^2\alpha\right)\left(1-sin^2\alpha\right)+\left(1+cot^2\alpha\right)\left(1-cos^2\alpha\right)=\dfrac{1}{cos^2\alpha}.cos^2\alpha+\dfrac{1}{sin^2\alpha}.sin^2\alpha=1+1=2\)