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SSC CGL 2023 PYQ — Question 54

SSC CGL - 21 July 2023 - Shift 2 • Quantitative Aptitude • Q54

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Find the value of 1−sin3θ1+sin3θ\sqrt{\frac{1-sin 3\theta }{1+sin 3\theta }}

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Correct answer: A

Explanation

The correct answer is option 1 i.e.  sec 3θ-tan 3θ.

1−sin3θ1+sin3θ\sqrt{\frac{1-sin 3\theta }{1+sin 3\theta }}

put θ = 15°

= 1−sin(3×15)1+sin(3×15)\sqrt{\frac{1-sin (3\times15) }{1+sin (3\times 15) }}

= 1−sin45o1+sin45o\sqrt{\frac{1-sin 45^o }{1+sin 45^o }}

= 1−(1/2)1+(1/2)\sqrt{\frac{1-(1/\sqrt2) }{1+(1/\sqrt2)}}  = 2−12+1\sqrt{\frac{\sqrt2 -1 }{\sqrt2 +1}} = (2−1)(2−1)(2+1)(2−1)\sqrt{\frac{(\sqrt2 -1)(\sqrt2 -1) }{(\sqrt2 +1)(\sqrt2 -1)}} = 2−1\sqrt2 -1

Now, we check the option 1 :  sec 3θ - tan 3θ 

Put θ = 15°

= sec (3 × 15)° - tan (3 × 15)°

= sec 45° - tan 45°

=  2−1\sqrt2 -1

Hence, sec 3θ - tan 3θ is the correct answer