If sec2θ = 4, then find the value of sin2θ + cosec (90 - θ) where 0° < θ < 90°.
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Correct answer: C
Explanation
Has been given :
sec²θ = 4, 0° < θ < 90°
According to the formula:
sec²θ = 1 / cos²θ
sin²θ + cos²θ = 1
cosec(90° − θ) = secθ
1/cos²θ = 4
cos²θ = 1/4
cosθ = 1/2
sin²θ = 1 − cos²θ
= 1 − 1/4
= 3/4
secθ = 1 / cosθ= 2
sin²θ + cosec(90° − θ)
= 3/4 + 2
= 11/4