Question

Given that ∝ is acute and tan ∝=3/4, can you prove that 3 sin(θ + ∝) +4 cos(θ + ∝) =5 cosθ ?

Answer 1

Given, `tan alpha = 3/4`

so, `sin alpha =3/5` and `cos alpha =4/5`

Given,
`3 sin (theta +alpha) + 4 cos (theta+alpha)`

`=3 sin theta cos alpha + 3 cos theta sin alpha + 4 cos theta cos alpha - 4 sin theta sin alpha`

putting the values we get,

`=12/5 sin theta +9/5 cos theta +16/5 cos theta - 12/5 sin theta`

`= 25/5 cos theta =5 cos theta`

PROVED