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SSC CPO 2020 PYQ — Question 141

SSC CPO - 23 Nov 2020 - Shift 2 • Quantitative Aptitude • Q141

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The value of sin⁡230+cos⁡260∘−sec⁡35∘.sin⁡55∘sec⁡60∘+csc⁡30∘\dfrac{{{{\sin }^2}30 + {{\cos }^2}60^\circ - \sec35^\circ .\sin55^\circ }}{{\sec60^\circ + \csc30^\circ }} is equal to :

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Correct answer: C

Explanation

The correct answer is option 3 i.e. - 18\frac{1}{8} 

sin⁡230+cos⁡260∘−sec⁡35∘.sin⁡55∘sec⁡60∘+csc⁡30∘\dfrac{{{{\sin }^2}30 + {{\cos }^2}60^\circ - \sec35^\circ .\sin55^\circ }}{{\sec60^\circ + \csc30^\circ }}

secθ = 1/cosθ

sec 35° = 1/cos35° = 1/cos(90 - 55°) = 1/sin55°

= 14+14−12+2\dfrac{\frac{1}{4}+\frac{1}{4}-1}{2+2}

= −124\dfrac{\frac{-1}{2}}{4}

= - 18\dfrac{1}{8}