Question

If 7 sin2 Ѳ + 3 cos2 Ѳ = 4 , show that tan Ѳ = 1/√3

Answer 1

7sin^2 Ѳ +3cos^2 Ѳ=4
4sin^2 Ѳ + 3sin^2 Ѳ + 3cos^2 Ѳ =4
4sin^2 Ѳ + 3(sin^2 Ѳ + cos^2 Ѳ )= 4
4sin^2 Ѳ + 3 = 4 (since, sin^2 Ѳ + cos^2 Ѳ =1)
4sin^2 Ѳ = 4-3 = 1
sin^2 Ѳ =1/4
sin Ѳ = √1/4 =1/2

therefore......
Ѳ= 30° (sin 30°=1/2)
thus ..
tan Ѳ =1/√3 = tan 30°
hence proved!!...

Answer 2

7sin^2 Ѳ +3cos^2 Ѳ=4

4sin^2 Ѳ + 3sin^2 Ѳ + 3cos^2 Ѳ =4

4sin^2 Ѳ + 3(sin^2 Ѳ + cos^2 Ѳ )= 4

4sin^2 Ѳ + 3 = 4 (since, sin^2 Ѳ + cos^2 Ѳ =1)

4sin^2 Ѳ = 4-3 = 1

sin^2 Ѳ =1/4

sin Ѳ = √1/4 =1/2

Ѳ= 30° (sin 30°=1/2)

tan Ѳ =1/√3 = tan 30°