Question

Given 5 Cos A - 12 Sin A = 0 , then evaluate the value of Sin A+Cos A by 2 Cos A− Sin A

Answer 1

If 5 cosA-12sinA=0, what is the value of sinA+cosA/2cosA-sinaA?

Let y=(sinA + cosA)/(2cosA-sinA)

Taking CosA as common from both numerator and denominator

y=[cosA((sinA/cosA)+(cosA/cosA))] /[cosA(2(cosA/cosA)-(sinA/cosA))]

Cancelling cosA and as we know sinA/cosA=tanA

So,

y=(tanA+1)/(2-tanA)

And we know

5cosA-12sinA=0

5cosA =12sinA

5=12[(sinA/cosA)]

TanA=5/12

Substitute the value of tanA in y

we get

y=(1+(5/12))/(2-(5/12))

y=[(12+5)/12]/[(12*2–5)/12]

Cancelling 12

y=17/(24–5)

y=17/19