If {(sin x)^4}/2 + {(cos x)^4}/3 = 1/5,then the value of (tan x)^2 is equal to-

{(sin x)^4}/2 + {(cos x)^4}/3 = 1/5By dividing (cosx)^4 we get{(Tanx)^4}/2 +1/3 = (1/5)(secx)^4{(Tanx)^4}/2 +1/3 = (1/5){1+ ( tanx)^2}^215(tanx)^4 +10 = 6{ 1+ (tanx)^4 + 2(tanx)^2 }9(tanx)^4 -12(tanx)^2 + 4 =0{3(tanx)^2 - 2 }^2 = 0(tanx)^2 =2/3

Approved