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Question

If cosθ+secθ=52, then the general value of θ is


A

nπ±π3

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B

2nπ±π6

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C

nπ±π6

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D

2nπ±π3

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Solution

The correct option is D

2nπ±π3


Explanation for the correct option:

Step 1. Find the value of θ:

Given, cosθ+secθ=52

cosθ+1cosθ=52

cos2θ+1=52cosθ

2cos2θ+2=5cosθ

2cos2θ5cosθ+2=0

2cos2θ4cosθcosθ+2=0

2cosθ(cosθ2)1(cosθ2)=0

(2cosθ1)(cosθ2)=0

cosθ=12,cosθ=2

Step 2. cosθ=2 is not possible since range of cosθ is [-1,1].

cosθ=12

cosθ=cosπ3

θ=2nπ±π3

Hence, Option ‘D’ is Correct.


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