a: Ta có: \(\sin^2a+cos^2a=1\)
=>\(cos^2a=1-\left(\frac12\right)^2=1-\frac14=\frac34\)
=>\(cosa=\frac{\sqrt3}{2}\)
\(\tan a=\frac{\sin a}{cosa}=\frac12:\frac{\sqrt3}{2}=\frac{1}{\sqrt3}\)
\(\cot a=\frac{1}{\tan a}=\sqrt3\)
b: \(\sin^2a+cos^2a=1\)
=>\(\sin^2a=1-0,8^2=1-0,64=0,36=0,6^2\)
=>sin a=0,6
\(\tan a=\frac{\sin a}{cosa}=\frac{0.6}{0.8}=\frac34\)
\(\cot a=\frac{1}{\tan a}=1:\frac34=\frac43\)
c: \(\tan a\cdot\cot a=1\)
=>\(cota=1:\frac34=\frac43\)
Ta có: \(1+\tan^2a=\frac{1}{cos^2a}\)
=>\(\frac{1}{cos^2a}=1+\left(\frac34\right)^2=1+\frac{9}{16}=\frac{25}{16}\)
=>\(cos^2a=\frac{16}{25}\)
=>\(cosa=\frac45\)
\(\sin^2a+cos^2a=1\)
=>\(\sin^2a=1-\frac{16}{25}=\frac{9}{25}\)
=>sin a=\(\frac35\)
d: \(\cot a\cdot\tan a=1\)
=>\(\tan a=1:\frac{\sqrt3}{3}=\frac{3}{\sqrt3}=\sqrt3\)
Ta có: \(1+\tan^2a=\frac{1}{cos^2a}\)
=>\(\frac{1}{cos^2a}=1+3=4\)
=>\(cos^2a=\frac14\)
=>cosa=1/2
Ta có: \(\sin^2a+cos^2a=1\)
=>\(sin^2a=1-\frac14=\frac34\)
=>sin a=\(\frac{\sqrt3}{2}\)
