General Aptitude TestQuantitative ReasoningTrigonometry

If ≤ft(cos ^2 θ-1)≤ft(1+tan ^2 θ)+2 tan ^2 θ=1,0^° < θ <90^° then θ i…

If $\left(\cos ^2 \theta-1\right)\left(1+\tan ^2 \theta\right)+2 \tan ^2 \theta=1,0^{\circ} < \theta <90^{\circ}$ then $\theta$ is:

Answer & explanation

Correct answer: option 4

( cos²θ - 1 ) .(1 + tan²θ) + 2tan²θ = 1

Using :-

sin²θ + cos²θ = 1

& sec²θ - tan²θ = 1

( - sin²θ ) .(sec²θ) + 2tan²θ = 1

- tan²θ + 2tan²θ = 1

tan²θ = 1

{ we know, tan45º = 1 }

So, θ = 45º