#### 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) = cosec^{2} θ

Sec θ = sec (90 – 60°)

On equating we get

Sec θ = sec 30°

𝜃 = 30°

To Find 2 cos^{2} 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

Solution 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.