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SSC CGL 2025 PYQ — Question 56

SSC CGL - 23 Sep 2025 - Shift 2 • Quantitative Aptitude • Q56

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If sin A = 45\frac{4}{5} and A lies in the 2nd quadrant, find the value of (1 + tan A)(1 - tan A)

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Correct answer: D

Explanation

The correct answer is option 4 i.e. −79-\frac{7}{9}.

sin A = 4/5, A lies in the second quadrant

In the second quadrant, cos A is negative

cos⁡A=−1−sin⁡2A\cos A = -\sqrt{1 - \sin^2 A}

=−1−(45)2= -\sqrt{1 - \left(\frac{4}{5}\right)^2}

=−1−1625= -\sqrt{1 - \frac{16}{25}}

=−925= -\sqrt{\frac{9}{25}}

=−35= -\frac{3}{5}

tan⁡A=sin⁡Acos⁡A=4/5−3/5=−43\tan A = \frac{\sin A}{\cos A} = \frac{4/5}{-3/5} = -\frac{4}{3}

⇒ tan⁡2A=(−43)2=169\tan^2 A = \left(-\frac{4}{3}\right)^2 = \frac{16}{9}

(1+tan⁡A)(1−tan⁡A)=1−tan⁡2A(1 + \tan A)(1 - \tan A) = 1 - \tan^2 A

=1−169=1 - \frac{16}{9}

=−79= -\frac{7}{9}