Question

if CotA=5/4 so find the value of 2sinA -3cosA /3sinA+2cosA

Answer 1

The answer is given below :

Given, cotA = 5/4

Now,

(2sinA - 3cosA)/(3sinA + 2cosA)

= (2 - 3cotA)/(3 + 2cotA), dividing both numerator and denominator by sinA, where sinA ≠ 0

= (2 - 15/4)/(3 + 10/4)

= {(8 - 15)/4}/{(12 + 10)/4}

= (-7/4)/(22/4)

= -7/22

Thank you for your question.

Answer 2

cotA=5/4
cosA/sinA=5/4
cosA=5sinA/4
NOW,
2sinA-3cosA=2sinA-(3×5sinA/4)=2sinA-15sinA/4
=8sinA-15sinA/4=-7sinA/4
3sinA+2cosA=3sinA+(2×5sinA/4)=3sinA+5sinA/2
=6sinA+5sinA/2=11sinA/2
Now,
2sinA-3cosA/3sinA+2cosA=-7sinA/4/11sinA/2=-7/22ans