Bài 1:
\(\sin^2a+cos^2a=1\)
=>\(cos^2a=1-\left(\frac35\right)^2=1-\frac{9}{25}=\frac{16}{25}\)
=>\(cosa=\frac45\)
\(\tan a=\frac{\sin a}{cosa}=\frac35:\frac45=\frac34\)
\(cota=1:\frac34=\frac43\)
BÀi 2:
a: \(A=\left(\sin a+cosa\right)^2+\left(\sin a-cosa\right)^2\)
\(=\sin^2a+cos^2a+2\cdot\sin a\cdot cosa+\sin^2a+cos^2a-2\cdot\sin a\cdot cosa\)
\(=1+2\cdot\sin a\cdot cosa+1-2\cdot\sin a\cdot cosa\)
=2
b: \(B=\sin a\cdot cosa\left(\tan a+\cot a\right)\)
\(=\sin a\cdot cosa\left(\frac{\sin a}{cosa}+\frac{cosa}{\sin a}\right)\)
\(=\sin a\cdot cosa\cdot\frac{\sin^2a+cos^2a}{\sin a\cdot cosa}=\sin^2a+cos^2a\)
=1
c: \(C=\cot^2a-cos^2a\cdot\cot^2a\)
\(=\cot^2a\left(1-cos^2a\right)\)
\(=\frac{cos^2a}{\sin^2a}\cdot\sin^2a=cos^2a\)
d: \(D=\tan^2a-\sin^2a\cdot\tan^2a\)
\(=\tan^2a\left(1-\sin^2a\right)\)
\(=\frac{\sin^2a}{cos^2a}\cdot cos^2a=\sin^2a\)
e: \(E=3\left(\sin^4a+cos^4a\right)-2\cdot\left(\sin^6a+cos^6a\right)\)
\(=3\cdot\left\lbrack\left(\sin^2a+cos^2a\right)^2-2\cdot\sin^2a\cdot cos^2a\right\rbrack-2\left\lbrack\left(\sin^2a+cos^2a\right)^3-3\cdot\sin^2a\cdot cos^2a\left(\sin^2a+cos^2a\right)\right\rbrack\)
\(=3\left\lbrack1-2\cdot\sin^2a\cdot cos^2a\right\rbrack-2\cdot\left\lbrack1-3\cdot\sin^2a\cdot cos^2a\right\rbrack\)
\(=3-6\cdot\sin^2a\cdot cos^2a-2+6\cdot\sin^2a\cdot cos^2a\)
=3-2
=1
