Trigonometry

Geometry Level 2

$\large \dfrac {4\tan^2 \theta}{\sec^4 \theta} = 1$

What is $\theta$ (which is in between 0 to 90 degrees)?

60^\circ

15^\circ

30^\circ

45^\circ

1 solution

Tasneem Khaled
Jul 26, 2017

4(tan θ)^2/(secθ)^4 = 1

or, 4(sinθ)^2(cosθ)^4/(cosθ)^2 = 1

or, 4(sinθcosθ)^2 = 1

or, 2(sinθcosθ) = 1

or, sin2θ = 1

or, 2θ = arcsin(1)

or θ = 90/2

or θ = 45