Question

if (x+2)sinA + (2x-1)cosA = 2x+1. Prove that tanA = 4/3 or 2x/x^2-1

Answer 1

(x+2) Sin A +(2x-1) Cos A = 2x+1--------1

we know that ,

 Sin A =(2 tan(A/2))/(1+tan2(A/2) and Cos A = (1-tan2(A/2))/(1+tan2(A/2)

let tan(A/2) = k and it in first equation

We get,

 (x+2)(2k)/(1+k2)  + (2x-1)(1-k2)/(1+k2) = 2x+1

(2x+4)k+(2x-1)-(2x-1)k2 = (2x+1)(1+k2)

(4x)k2-(2x+4)k+2=0  ---------2

By solving eq 2 we get,

k=1/x or k=0.5

tan(A/2)=1/m or tan(A/2) =0.5

A/2 = tan ⁻¹(1/x) 0r A/2 =tan ⁻¹(0.5)

A=2tan ⁻¹(1/x) or 53.130102354

 
tan A=tan (2tan ⁻¹(1/x) or 4/3