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If 0 ≤ θ ≤ $$\frac{\pi }{2}$$ and sec2θ + tan2θ = 7, then θ is
Answer & Solution
Correct Answer:
Option
B
sec2θ + tan2θ = 7
1 + tan2θ + tan2θ = 7
2tan2θ = 7 - 1 = 6
tan2θ = 3
tanθ = √3 = tan 60°
$$\eqalign{ & \because {180^ \circ } = \pi {\text{ radian}} \cr & \therefore {60^ \circ } = \frac{\pi }{{180}} \times 60 = \frac{\pi }{3}{\text{ radian}} \cr} $$
1 + tan2θ + tan2θ = 7
2tan2θ = 7 - 1 = 6
tan2θ = 3
tanθ = √3 = tan 60°
$$\eqalign{ & \because {180^ \circ } = \pi {\text{ radian}} \cr & \therefore {60^ \circ } = \frac{\pi }{{180}} \times 60 = \frac{\pi }{3}{\text{ radian}} \cr} $$
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