Question

a) Rút gọn \(P=cos^2a+cos^2a.cot^2a\) ( 0 độ < a < 90 độ )

b) Rút gọn \(M=\frac{2cos^2a-1}{sina+cosa}\)

Answer 1

\(P=cos^2a\left(1+cot^2a\right)=\dfrac{cos^2a}{sin^2a}=cot^2a\)

\(M=\dfrac{2cos^2a-\left(sin^2a+cos^2a\right)}{sina+cosa}=\dfrac{cos^2a-sin^2a}{sina+cosa}\)

\(=\dfrac{\left(cosa-sina\right)\left(cosa+sina\right)}{sina+cosa}=cosa-sina\)