\frac{2 \left(tan\right)^{2} 30 º \left(sec\right)^{2} 52 º \left(sin\right)^{2} 38 º}{\left(cosec\right)^{2} 70 º

Foundation

Mathematics Foundation

Introduction to Trigonometry

Question

$\frac{2 \tan^{2} 30 º \sec^{2} 52 º \sin^{2} 38 º}{{cosec}^{2} 70 º - \tan^{2} 20 º} = ?$

$\frac{2}{3}$

$\frac{3}{2}$

$\frac{1}{2}$

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Given expression $= \frac{2 \times {(\frac{1}{\sqrt{3}})}^{2} \sec^{2} 52 º \sin^{2} (90 º - 52 º)}{{cosec}^{2} 70 º - \tan^{2} (90 º - 70 º)} = \frac{2}{3} \cdot \frac{\sec^{2} 52 º \cos^{2} 52 º}{({cosec}^{2} 70 º - \cot^{2} 70 º)}$

$= \frac{2}{3} \times \frac{1}{1} = \frac{2}{3}$