Question

(m+2)sin α+(2m-1)cosα=2m+1​

Answer 1

Hey mate ☺️

(m+2) Sin a +(2m-1) Cos a= 2m+1--------1we 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 equationWe get, (m+2)(2k)/(1+k2) + (2m-1)(1-k2)/(1+k2) = 2m+1(2m+4)k+(2m-1)-(2m-1)k2 = (2m+1)(1+k2)(4m)k2-(2m+4)k+2=0 ---------2By solving eq 2 we get,k=1/m or k=0.5tan(a/2)=1/m or tan(a/2) ==0.5A/2 = tan ⁻¹(1/m) 0r A/2 =tan ⁻¹(0.5)A=2tan ⁻¹(1/m) or 53.130102354 tan A=tan (2tan ⁻¹(1/m) or 4/3

I Hope it helps you ☺️✌️✌️