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SSC CGL 2022 PYQ — Question 62

SSC CGL - 06 Dec 2022 - Shift 1 • Quantitative Aptitude • Q62

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cos20°sin70°+cosθsin(90°−θ)={{cos20°} \over sin70°}+{{cos\theta} \over sin(90°-\theta)}=________________.

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Correct answer: D

Explanation

The correct answer is Option 4 i.e. 2.

Concept Used:

cos⁡(90−θ)=sin⁡θ\cos(90 - \theta) = \sin\theta

Explanation:

according to the given question,

cos20°sin70°+cosθsin(90°−θ){{cos20°} \over sin70°}+{{cos\theta} \over sin(90°-\theta)}

⇒ cos⁡(90−70)°sin⁡70°+cos⁡θcos⁡θ{{\cos(90 - 70)°} \over \sin70°}+{{\cos\theta} \over \cos\theta}

⇒ sin⁡70sin⁡70+1{\sin 70 \over \sin 70} + 1 = 1 + 1 = 2

Hence the value of cos20°sin70°+cosθsin(90°−θ){{cos20°} \over sin70°}+{{cos\theta} \over sin(90°-\theta)}  is 2.