Question

∆if tan theta is equal to 3 by 4 find 5 sin theta minus 3 cos theta by 5 sin theta + 3 cos theta​

Answer 1

Answer:it is solved below

Step-by-step explanation:

Given that, tan theta =3/4=(p/b)

Now,h=√p^2+b^2=√3^2+4^2=5

Sin theta= p/h =3/5

Cos theta =b/h=4/5

Now,

(5sin theta -3cos theta)/(5sin theta+3 cos theta)=?

Rationalizing we get,

(5 sin theta- 3 cos theta)^2/25 sin^2 theta-9cos^2theta

=(25 sin^2 theta+9 cos^2 theta-30 sin theta cos theta)/ 25 sin^2 theta - 9 cos^2 theta

=25(9/25)+9(16/25)-30(3/5)(4/5)÷[25(9/25)-9(16/25)]

=9+(96/25)-(72/5)÷[9-(96/25)]

Solve it and get the answer.