Is the answer 4/3?

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Is the answer 4/3?

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4sinα+3cosα= 5

dividing the both sides by cosα

squaring

16tan²α + 9 + 24tanα = 25tan²α + 25

9tan²α - 24tanα + 16 = 0

(3tanα)² - 2 . 3tanα .4 + 4² = 0

(3tanα - 4)² = 0

tanα = 4/3__ANSWER__

dividing the both sides by cosα

squaring

16tan²α + 9 + 24tanα = 25tan²α + 25

9tan²α - 24tanα + 16 = 0

(3tanα)² - 2 . 3tanα .4 + 4² = 0

(3tanα - 4)² = 0

tanα = 4/3

or sina=(5-3cosa)/4

sina*sina=((5-3cosa)/4)((5-3cosa)/4)=(25+9(cosa*cosa)-30cosa)/16

But sina*sina + cosa*cosa =1

So (25 +9(cosa*cosa)-30cosa)/16 +cosa*cosa =1

Simplifying we get 25(cosa*cosa) -30cosa + 9 =0

or 25(cosa*cosa) -15cosa -15cosa +9 =0

or 5cosa(5cosa - 3) -3(5cosa - 3) = 0

or (5cosa - 3)(5cosa -3) = 0

or 5cosa -3 = 0

or cosa = 3/5

So sina = (5 - 3(3/5))/4 = 4/5

So tana=sina/cosa = (4/5)/(3/5) = 4/3