Question

If 5 tan A = 4, then what is the value of 5sin A -3 cos A ÷ sin A+2 cos A?

Answer 1

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5 tan A = 4

Therefore tan A = 4/5

5sin A -3 cos A ÷ sin A+2 cos A

=> 5sin A / cos A  -3 cos A / cos A / sin A / cos A +2 cos A / cos A

( Dividing the  numerator and Denominator by cos A)

=> 5 tan A - 3 / 5 tan A + 2

=> 5 * 4/5 - 3 / 5 * 4/5 + 2 (Substituting tan A = 4/5)

=> 4 - 3/ 4 - 2 = 1/6 (Answer)