The expression ((1-2 sin²θ cos² θ)(cot θ +1)cos θ)/((sin⁴ θ + cos⁴ θ )(1+tan θ)cosec θ)-1, 0⁰, equals:

The expression ((1-2 sin²θ cos² θ)(cot θ +1)cos θ)/((sin⁴…

The expression $\frac{(1-2 sin^2\theta cos^2 \theta)(cot \theta +1)cos \theta}{(sin^4 \theta + cos^4 \theta )(1+tan \theta)cosec \theta}-1, 0^0<\theta < 90^0$ , equals:

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Correct answer: B

Explanation

The correct answer is option 2 i.e. -sin² $\theta$

Shortcut : put $\theta$ = 45° (0 < $\theta$ < 90)

on putting $\theta$ = 45 we get,

[(1 - 2 × 1/2 × 1/2)(1 + 1) × 1/ $\sqrt2$ ]/[(1/4 + 1/4)(1 + 1)( $\sqrt2$ )] - 1

1/2 - 1 = 1/2

Now put $\theta$ = 45° in option as well

Option 1 = cos² 45 = 1/2

Option 2 = -sin² 45 = -1/2 ( matches with the answer)

Option 3 = sec² 45 = 2

Option 4 = -sec² 45 = -2.

SSC CGL 2022 PYQ — Question 3