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Question
Which of the following is true for all values of θ (0° ≤ θ ≤ 90°)?
Options
cos2 θ – sin2 θ = 1
cosec2 θ – sec2 θ = 1
sec2 θ – tan2 θ = 1
cot2 θ – tan2 θ = 1
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Solution
sec2 θ – tan2 θ = 1
Explanation:
∵ sec2 θ = 1 + tan2 θ
∴ sec2 θ – tan2 θ = 1
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RELATED QUESTIONS
Prove that (1 + cot θ – cosec θ)(1+ tan θ + sec θ) = 2
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If cot θ = `40/9`, find the values of cosec θ and sinθ,
We have, 1 + cot2θ = cosec2θ
1 + `square` = cosec2θ
1 + `square` = cosec2θ
`(square + square)/square` = cosec2θ
`square/square` = cosec2θ ......[Taking root on the both side]
cosec θ = `41/9`
and sin θ = `1/("cosec" θ)`
sin θ = `1/square`
∴ sin θ = `9/41`
The value is cosec θ = `41/9`, and sin θ = `9/41`
