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SSC CGL 2023 PYQ — Question 54

SSC CGL - 26 July 2023 - Shift 3 • Quantitative Aptitude • Q54

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If cos⁡x+sec⁡x=723\cos x + \sec x = \frac{7}{2\sqrt{3}}, then the value of cos2 x + sec2 x will be ______.

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 2512\frac{25}{12}.

Given that

cos⁡x+sec⁡x=723\cos x + \sec x = \frac{7}{2\sqrt{3}}

Squaring both sides we get

cos2x+sec⁡2x+2=(723)2\\cos^2x + \sec^2 x + 2 = (\frac{7}{2\sqrt{3}})^2

cos2x+sec⁡2x=(723)2−2\\cos^2x + \sec^2 x = (\frac{7}{2\sqrt{3}})^2 - 2 = 2512\frac{25}{12}