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Question
If θ is a positive acute angle such that sec θ = cosec 60°, find 2 cos2 θ – 1
Solution
We know that sec (90 – θ) = cosec2 θ
Sec θ = sec (90 – 60°)
On equating we get
Sec θ = sec 30°
𝜃 = 30°
To Find 2 cos2 θ – 1
`=> 2 xx cos^2 30^@ - 1` `[cos 30 = sqrt3/2]`
`=> 2 xx (sqrt3/2)^2 - 1`
`=> 2 xx 3/4 - 1`
`=> 3/2 - 1`
`= 1/2`
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