Question

Is sinA+sin2A=x,cosA+cos2A=y then cosA=

Answer 1

https://www.sscias.com/2018/08/mathematics-today-magazine-august-2018.html?m=1

Answer 2

sinA+sin2A=x⇒sinA+2sinA.cosA=x⇒sinA(1+2cosA)=x....(i)cosA+cos2A=y⇒cosA+2cos2A−1=y⇒cosA+2cos2A=y+1⇒cosA(1+2cosA)=y+1....(ii)sinA(1+2cosA)cosA(1+2cosA)=xy+1⇒tanA=xy+1⇒tan2A=(xy+1)2⇒sec2A−1=x2(y+1)2  [sec2θ−tan2θ=1]⇒sec2A=x2(y+1)2+1⇒sec2A=x2+(y+1)2(y+1)2⇒cos2A=(y+1)2x2+(y+1)2cosA=±(y+1)x2+(y+1)2√