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SSC CGL 2022 PYQ — Question 65

SSC CGL - 11 April 2022 - Shift 1 • Quantitative Aptitude • Q65

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The value of sin⁡23∘cos⁡67∘+sec⁡52∘sin⁡38∘+cos⁡23∘sin⁡67∘+csc⁡52∘cos⁡38∘csc⁡220∘−tan⁡270∘\frac{\sin 23^\circ \cos 67^\circ + \sec 52^\circ \sin 38^\circ + \cos 23^\circ \sin 67^\circ + \csc 52^\circ \cos 38^\circ}{\csc^2 20^\circ - \tan^2 70^\circ}  is:

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 3.

= sin⁡23∘cos⁡67∘+sec⁡52∘sin⁡38∘+cos⁡23∘sin⁡67∘+csc⁡52∘cos⁡38∘csc⁡220∘−tan⁡270∘\frac{\sin 23^\circ \cos 67^\circ + \sec 52^\circ \sin 38^\circ + \cos 23^\circ \sin 67^\circ + \csc 52^\circ \cos 38^\circ}{\csc^2 20^\circ - \tan^2 70^\circ}

Sin23° cos67° + sec52° sin38 + cos23° sin67° + cosec52° cos38°)/(cosec220° - tan270°)

(Sin23° cos67° + cos23° sin67°) + (cosec38° sin38 + sec38° cos38°))/(cosec220° - tan270°)

((Sin(23 + 67)) + 1 + 1)/(sec270° - tan270°)

(Sin90° + 2)/1

(1 + 2) = 3