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If θ is a Positive Acute Angle Such that Sec θ = Cosec 60°, Find 2 Cos2 θ – 1 - Mathematics

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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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APPEARS IN

 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 10: Trigonometric Ratios
Ex. 10.3 | Q: 13 | Page no. 54
 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 10: Trigonometric Ratios
Ex. 10.3 | Q: 13 | Page no. 54
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If θ is a Positive Acute Angle Such that Sec θ = Cosec 60°, Find 2 Cos2 θ – 1 Concept: Trigonometric Ratios of an Acute Angle of a Right-angled Triangle.
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