Question

9cosA+12sinA=15then find the value of cotA

Answer 1

let 9= asint and 12= acost
a^2 (sin^2 t+cos^2 t)=9^2+12^2=81+144=225
or a^2=225
or a=15
now 9cosA+12sinA=15
or asintcosA+acostsinA=15
or asin (t+A)=15
or 15sin (t+A)=15
or sin (t+A)=1=sin 90
or t+A=90
A=90-t
so cotA = cot (90-t)=tan t=sint/cost
=asint/acost=9/12=3/4