Question

please please give me the correct answer

Answer 1

2Sinx + 3cosx = 3

2sinx = 3 - 3cosx

squaring both sides

4sin^2x = 9 + 9cos^2x - 18cosx

4 - 4cos^2x = 9 + 9cos^2x - 18cosx

13cos^2x - 18cos x + 5 = 0

13cos^2x -13cosx -5cosx + 5 = 0

13cosx(cosx -1) -5(cosx-1)= 0

(13cosx -5) (cosx -1) = 0

cosx = 5/13 or cosx = 1

if cos x = 1

2Sinx + 3cosx = 3

2sinx + 3 = 3

2sinx = 0

sinx = 0

tanx = sinx/cosx = 0

cosx = 5/13

2Sinx + 3cosx = 3

2sinx + 3(5/13) = 3

2sinx + 15/13 = 3

2sinx = 24/13

sinx = 12/13

tanx = sinx/cosx = 12/5

Answer 2

$\green{ \fcolorbox{grey}{grey}{ \checkmark \: \textsf{Verified \: answer}}}$

Tan Q = 12/5