Question

if 7sin^2x+3 cos^2x=4 show that tanx=1/√3​

Answer 1

Step-by-step explanation:

Step-by-step explanation:7sin^2x+3 cos^2x=4

=> 4 sin^2 x + 3sin2x+3 cos^2x=4

=> 4 sin^2 x + 3sin2x+3 cos^2x=4=>4 sin^2 x+3( sin^2 x + cos^2 x)=4

=> 4 sin^2 x + 3sin2x+3 cos^2x=4=>4 sin^2 x+3( sin^2 x + cos^2 x)=4=>4sin^2 x +3(1)=4. [••• sin^2x + cos^2 x =1]

=>4 sin^2 x +3=4

=>4sin^2 x=4-3

=>4 sin^2 x=1

=> sin^2 x=1/4

=> sin x=√(1/4)

therefore, sin x =1/2

but, sin 30°=1/2

then, sin x = sin x30°

therefore, x=30°

Then, tan 30°=1/3

Hence, it is proved