Question

If 7 sin2theta + 3 cos2 theta=4 show that tan theta = 1/root3

Answer 1

7sin2ϴ + 3cos2ϴ = 4

4sin2 ϴ + 3sin2 ϴ+ 3cos2 ϴ = 4

4sin2 ϴ +3 (sin2 ϴ + cos2 ϴ) = 4

4sin2 ϴ + 3 = 4

4sin2 ϴ = 1 

sin2 ϴ =1/4 

sin ϴ = ½

sin ϴ =perp./hypo. = ½

So, perp. = 1k  ; hypo. = 2k

(Hypo)2  = (base)2 + (perp.)2

k2 = (base)2 + (2k)2

(base)2 = 4k2 – k2

base =  root3 k

tan ϴ = perp./base = k/root3 k

so, tan ϴ =1/root3

Hope it helps !!!!!!!!!!!!!!!!!!!!!!!!!

Answer 2

7sin²θ + 3cos²θ = 4
7sin²θ + ౩(1-sin²θ) = 4
7sin²θ+3-3sin²θ = 4
4sin²θ+3 = 4
4sin²θ=1
sin²θ = 1/4
sinθ = +1/2
sinθ = +  π/6
Therefore tan θ = + π/6
then we get tan θ = + 1/√3