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Question : The value of $\frac{3\left(\operatorname{cosec}^2 26^{\circ}-\tan ^2 64^{\circ}\right)+\left(\cot ^2 42^{\circ}-\sec ^2 48^{\circ}\right)}{\cot \left(22^{\circ}-\theta\right)-\operatorname{cosec}^2\left(62^{\circ}+\theta\right)-\tan \left(\theta+68^{\circ}\right)+\tan ^2\left(28^{\circ}-\theta\right)}$ is:

Option 1: 3

Option 2: 4

Option 3: –1

Option 4: –2


Team Careers360 21st Jan, 2024
Answer (1)
Team Careers360 23rd Jan, 2024

Correct Answer: –2


Solution : $\frac{3\left(\operatorname{cosec}^2 26^{\circ}-\tan ^2 64^{\circ}\right)+\left(\cot ^2 42^{\circ}-\sec ^2 48^{\circ}\right)}{\cot \left(22^{\circ}-\theta\right)-\operatorname{cosec}^2\left(62^{\circ}+\theta\right)-\tan \left(\theta+68^{\circ}\right)+\tan ^2\left(28^{\circ}-\theta\right)}$
$= \frac{3\left(\operatorname{sec}^2 64^{\circ}-\tan ^2 64^{\circ}\right)+\left(\cot ^2 42^{\circ}-\operatorname{cosec} ^2 42^{\circ}\right)}{\tan \left(68^{\circ}+\theta\right)-\operatorname{cosec}^2\left(62^{\circ}+\theta\right)-\tan \left(\theta+68^{\circ}\right)+\cot ^2\left(62^{\circ}+\theta\right)}$
$= \frac{3\left(1\right)+\left(\cot ^2 42^{\circ}-1-\cot ^2 42^{\circ}\right)}{-(\operatorname{cosec}^2\left(62^{\circ}+\theta\right)-\cot ^2\left(62^{\circ}+\theta\right))}$
$= \frac{3-1}{-1}$
$= -2$
Hence, the correct answer is –2.

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