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If (cosθ + secθ) = 5/2 then(cos^2θ + sec^2θ) = ?

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If (cosθ + secθ) = 5/2 then(cos2θ + sec2θ) = ?

(a) 21/4 

(b) 17/4 

(c) 29/4 

(d) 33/4

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Correct answer is (b) 17/4

We have (cos θ + sec θ) = 5/2 

Squaring both sides, we get: 

(Cos θ + sec θ)2 = (5/2)2 

⇒ cos2 θ + sec2 θ + 2θ = 25/4 

⇒ cos2 θ + sec2 θ + 2 = 25/4 [∵ sec θ = 1/cos θ] 

⇒ cos2 θ + sec2 θ = 25/4 − 2 = 17/4

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