đáp án không giống lắm 

Dạ em cảm ơn ạ

\(A=\frac{\frac{3sina}{cosa}+\frac{2cosa}{cosa}}{\frac{3sina}{cosa}-\frac{2cosa}{cosa}}=\frac{3tana+2}{3tana-2}=\frac{24+2}{24-2}=\frac{26}{22}=\frac{13}{11}\)

Lời giải:

$\cos ^2a=1-\sin ^2a=1-(\frac{1}{2})^2=\frac{3}{4}$

$\Rightarrow \cos a=\pm \frac{\sqrt{3}}{2}$

Nếu $\cos a=\frac{\sqrt{3}}{2}$ thì:

$A=3\sin a+4\cos a=3.\frac{1}{2}+4.\frac{\sqrt{3}}{2}=\frac{3+4\sqrt{3}}{2}$

Nếu $\cos a=\frac{-\sqrt{3}}{2}$ thì:

$A=3\sin a+4\cos a=3.\frac{1}{2}+4.\frac{-\sqrt{3}}{2}=\frac{3-4\sqrt{3}}{2}$

1: \(sin^6x+cos^6x+3sin^2x\cdot cos^2x\)

\(=\left(sin^2x+cos^2x\right)^2-3\cdot sin^2x\cdot cos^2x\cdot\left(sin^2x+cos^2x\right)+3\cdot sin^2x\cdot cos^2x\)

=1

2: \(sin^4x-cos^4x\)

\(=\left(sin^2x+cos^2x\right)\left(sin^2x-cos^2x\right)\)

\(=1-2\cdot cos^2x\)

\(P=3sin^22a+4cos^22a\)

\(\Rightarrow P=3sin^22a+3cos^22a+cos^22a\)

\(\Rightarrow P=3\left(sin^22a+cos^22a\right)+\left(2cos^2a-1\right)^2\)

\(\Rightarrow P=3.1+\left(2.\dfrac{1}{9}-1\right)^2\left(cosa=\dfrac{1}{3}\right)\)

\(\Rightarrow P=3+\left(-\dfrac{7}{9}\right)^2\)

\(\Rightarrow P=3+\dfrac{49}{81}\)

\(\Rightarrow P=\dfrac{292}{81}\)