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SSC CPO 2023 PYQ — Question 128

SSC CPO - 03 Oct 2023 - Shift 3 • Quantitative Aptitude • Q128

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If sin θ\theta + cos θ\theta = 113\frac{\sqrt{11}}{3}, then the value of (cos θ\theta - sin θ\theta) is:

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 73\frac{\sqrt{7}}{3}

Given that

If sin θ\theta + cos θ\theta = 113\frac{\sqrt{11}}{3},

Squaring both sides,

⇒ (sin θ\theta + cos θ\theta )2 = 119\frac{{11}}{9},

⇒ sin2 θ\theta + cos2 θ\theta + 2 sin θ\thetacos θ\theta = 119\frac{{11}}{9}

⇒ 1 +  2 sin θ\thetacos θ\theta = 119\frac{{11}}{9}

⇒ 2 sin θ\thetacos θ\theta = 119\frac{{11}}{9} - 1 = 2/9

 As we know,

⇒ (cos θ\theta - sin θ\theta)2 =  sin2 θ\theta + cos2 θ\theta - 2 sin θ\thetacos θ\theta = 1 -  2 sin θ\thetacos θ\theta = 1 - 2/9 = 7/9

 Hence, cos θ\theta - sin θ\theta = 73\frac{\sqrt{7}}{3}