Question

If 5 tan theta is equal to 4 then find the value of 5 sin theta - 3 cos

Answer 1

From 5 tan theta= 4,

we get,

5 (sin theta/cos theta)= 4

5 sin theta = 4 cos theta.--------A

question is 5 sin theta-3 cos theta=X

substituting A in 5 sin theta here,

4cos theta -3 cos theta=X

cos theta=X

Answer 2

tan theta =4/5

we know that tan theta = P/B

therefore hypotenuse (H) = √(4^2+5^2)

=3

sin theta =P/H

= 4/3

cos theta =B/ H

=5/3

5sin theta - 3 cos theta=20/3-5

= (20 - 15) /3

=5/3