If tan theta= 3/4 , find csc theta

Answer: [tex]csc\theta=\frac{5}{3}[/tex]Step-by-step explanation:Given:[tex]tan\theta =\frac{3}{4}[/tex][tex]cot\theta =\frac{4}{3}[/tex]                 [∵ [tex]cot\theta =\frac{1}{tan\theta}[/tex] ]Squaring both sides.[tex]cot^2\theta =\frac{4^2}{3^2}=\frac{16}{9}[/tex][tex]csc^2\theta -1=\frac{16}{9}[/tex]        [∵ [tex]cot^2\theta =csc^2\theta-1][/tex] ]Adding 1 to both sides.[tex]csc^2\theta -1+1=\frac{16}{9}+1[/tex][tex]csc^2\theta =\frac{16}{9}+1[/tex][tex]csc^2\theta=\frac{16}{9} +\frac{9}{9} [/tex]     [Taking LCD=9 and adding fractions ][tex]csc^2\theta=\frac{16+9}{9}[/tex] [tex]csc^2\theta=\frac{25}{9}[/tex] Taking square root both sides.[tex]\sqrt{csc^2\theta}=\sqrt{\frac{25}{9}}[/tex]∴ [tex]csc\theta=\frac{5}{3}[/tex]