Question

Giúp mình câu 15 16 với

Answer 1

Câu 15 : \(P=tan^3a+cot^3a+tan^2a+cot^2a=\left(tana+cota\right)^3-3tana.cota\left(tana+cota\right)+\left(tana+cota\right)^2-2tana.cota\)

\(=3^3-3.3+3^2-2=25\) . Chọn A 

Câu 16 : Đặt a = \(sin^2x;b=cos^2x\Rightarrow a+b=1\)

Ta có :  \(3a^2+b^2=\dfrac{3}{4}\) \(\Leftrightarrow3a^2+\left(1-a\right)^2=\dfrac{3}{4}\Leftrightarrow4a^2-2a+\dfrac{1}{4}=0\Leftrightarrow\left(a-\dfrac{1}{4}\right)^2=0\Leftrightarrow a=\dfrac{1}{4}\) 

Suy ra : \(a^2=\dfrac{1}{16}\Rightarrow b^2=\dfrac{9}{16}\)

\(P=sin^4x+3cos^4x=a^2+3b^2=\dfrac{1}{16}+3.\dfrac{9}{16}=\dfrac{7}{4}\)  . Chọn C