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SSC CGL 2023 PYQ — Question 61

SSC CGL - 21 July 2023 - Shift 3 • Quantitative Aptitude • Q61

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If cosαsinβ=10 and cosαcosβ=11\frac{cos \alpha}{sin \beta}=10 \ and \ \frac{cos \alpha}{cos \beta}=11   then the value of cos2βcos2 \beta = 11, then the value of cos²ẞ is:

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Correct answer: B

Explanation

The correct answer is option 2 i.e.  100221\frac{100}{221}

Given:

cosαsinβ=10\frac{cos \alpha}{sin \beta}=10                 ----------------(1)

and

cosαcosβ=11 \frac{cos \alpha}{cos \beta}=11                 ---------------(2)

From the first equation:

cos⁡ α\alpha = 10 sin β\beta⁡                   (Equation 1)

From the second equation:

cos⁡ α\alpha = 11 cos⁡  β\beta                (Equation 2)

From Equation 1 and Equation 2:

 10 sin β\beta⁡   =  11 cos⁡  β\beta

 sin β\beta⁡/ cos⁡ β\beta = 11/10

tan β\beta = 11/10

cos2β^2 \beta = 11+tan2β\frac{1}{1+tan^2 \beta}

Put the value of tan β\beta = 11/10​:

tan2β^2 \beta = (11/10​)2^2 = 121/100

cos2β^2 \beta = 11+121100=1221100=100221\frac{1}{1+\frac{121}{100}} = \frac{1}{\frac{221}{100}} = \frac{100}{221}