a) `sin^2 a+cos^2=1`
$\Rightarrow 0,8^2+\cos^2a=1$
$\Rightarrow \cos^2 a=\dfrac{9}{25}$
`⇒ cos a=\pm\frac{3}{5}`
`tan a=\frac{sin a}{cos a}=\pm\frac{\frac{4}{5}}{\frac{3}{5}}=\pm\frac{4}{3}`
`cot a=\frac{cos a}{sin a}=\pm\frac{\frac{3}{5}}{\frac{4}{5}}=\pm\frac{3}{4}`
b) `sin^2 a+cos^2=1`
`⇒ sin^2 a=1-\frac{9}{25}`
$\Rightarrow\sin a=\pm\frac{4}{5}$
`tan a=\frac{sin a}{cos a}=\pm\frac{\frac{4}{5}}{\frac{3}{5}}=\pm\frac{4}{3}`
`cot a=\frac{cos a}{sin a}=\pm\frac{\frac{3}{5}}{\frac{4}{5}}=\pm\frac{3}{4}`
c) `tan a. cot a=1`
`⇒ cot a =\frac{1}{3}`
`1+tan^2 a=\frac{1}{cos^2 a}`
`⇔ 1+9=\frac{1}{cos^2 a}`
$\Rightarrow\cos^2a=\dfrac1{10}$
`⇒ cos a=\pm\sqrt{10}/10`
`sin^2 a+ cos^2 a =1`
$\Rightarrow \sin^2a+\dfrac1{10}=1$
$\Rightarrow\sin^2a=\dfrac{9}{10}$
`⇒ sin a=\pm\frac{3\sqrt{10}}{10}`
d) `tan a. cot a=1`
`⇒ tan a =\frac{1}{2}`
`1+tan^2 a=\frac{1}{cos^2 a}`
`⇔ 1+\frac{1}{4}=\frac{1}{cos^2 a}`
$\Rightarrow\cos^2a=\dfrac45$
`⇒ cos a=\pm(2\sqrt{5})/5`
`sin^2 a+ cos^2 a =1`
$\Rightarrow\sin^2x+\dfrac45=1$
$\Rightarrow\sin^2x=\dfrac15$
`⇒ sin a=\pm\frac{\sqrt{5}}{5}`
