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CGP EDU Academic Team
Published on: August 13, 2026
Number of values of θ between 0 ° and 90 ° which satisfy the equation sec 2 θ .cosec 2 θ + 2 cosec 2 θ = 8
Text Solution
Verified by ExpertsThe correct answer is:
2
(2)
sec 2 θ .cosec 2 θ + 2 cosec 2 θ = 8 ⇒ 
= 8
⇒ 1 + 2 cos 2 θ = 8 sin 2 θ cos 2 θ ⇒ 8sin 2 θ cos 2 θ – 2cos 2 θ –1 = 0
⇒ 8(1 – cos 2 θ ) cos 2 θ –2 cos 2 θ – 1 = 0 ⇒ 8cos 4 θ – 6cos 2 θ + 1= 0
⇒ cos 2 θ = 
, 
= 
, 
⇒ cos θ = 
, 
⇒ θ = 45 o , 60 o in (0 o , 90 o )
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