Question

if 5tan theta=4, show that 5sin theta - 3cos theta/5sin theta + 2cos theta = 1/6

Answer 1

hey there is your answer..

if 5 tan  = 4

then

tan = 4/5

 

now

(5 sin – 3cos) / (5 sin + 2cos)

divide by cos  in both numerator and denominator

(5 tan – 3) / (5 tan + 2)

 put the value of tan 

(4 – 3) / (4 + 2)

 = 1/6

 

Answer 2

5tan theta =4. So, tan theta= 4/5.    Tan theta = sin theta÷cos theta .so, the cos theta =5 and sin theta = 4. Therefore, 5sintheta -3cos theta/5sin theta +cos theta=5(4)-3(5)/5(4)+2(5)=5/30=1/6