Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

If sec theta + tan theta = k, then cos theta equals

If sec θ + tan θ = k, then cos θ equals

1) (k2 + 1)/2k

2) 2k/(k2 + 1)

3) k/(k2 + 1)

4) k/(k2 – 1)

Answer: (2) 2k/(k2 + 1)

Solution:

Given,

sec θ + tan θ = k….(i)

We know that,

sec2θ – tan2θ = 1

(sec θ + tan θ)(sec θ – tan θ) = 1

k(sec θ – tan θ) = 1

sec θ – tan θ = 1/k….(ii)

Adding (i) and (ii),

2 sec θ = k + (1/k)

2/cos θ = (k2 + 1)/k

⇒ 2k = (k2 + 1) cos θ

⇒ cos θ = 2k/(k2 + 1)

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