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SSC CGL 2024 PYQ — Question 57

SSC CGL - 23 Sep 2024 - Shift 3 • Quantitative Aptitude • Q57

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The value of sin2θ−2sin4θ2cos4θ+cos2θ\frac{sin^2θ - 2sin^4θ}{2cos^4θ + cos^2θ} at θ = 45° is :

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Correct answer: B

Explanation

The correct answer is option 2 i.e 0.

sin2θ−2sin4θ2cos4θ+cos2θ\frac{sin^2θ - 2sin^4θ}{2cos^4θ + cos^2θ}

=sin245∘−2sin445∘2cos445∘+cos245∘=\frac{sin^245^\circ - 2sin^445^\circ}{2cos^445^\circ + cos^245^\circ}

 

= (12)2−2(12)42(12)4+(12)2\frac{(\frac{1}{\sqrt2})^2-2(\frac{1}{\sqrt2})^4}{2(\frac{1}{\sqrt2})^4+(\frac{1}{\sqrt2})^2}

= (1/2 - 1/2)/(1/2 + 1/2)

= 0/1 = 0

Therefore, the value of the expression at θ = 45° is 0.