If $7 \sin^2 \theta + 3 \cos^2 \theta = 4, 0^\circ < \theta < 90^\circ$, then the value of tanθ is:
Answer & explanation
Correct answer: option 2
7 sin²θ + 3 cos²θ = 4
4 sin²θ + 3 sin²θ + 3 cos²θ = 4
{ using , sin²θ + cos²θ = 1 } \
4 sin²θ + 3 = 4
Sinθ = \(\frac{ 1}{2}\)
{ using , Sin30º = \(\frac{ √3}{2}\) }
So, θ = 30º
tanθ
= tan30º
= \(\frac{ 1}{√3}\)