The value of ^2(^(-1)2) + cosec^2(^(-1)3) is: Option 1: 9 Option 2: 5 Option 3: 10 Option 4: 15

Answer: 15. Solution: Let _1 = ^(-1)2, so _1 = 2. Then ^2_1 = 1 + ^2_1 = 1 + 4 = 5. Let _2 = ^(-1)3, so _2 = 3. Then cosec^2_2 = 1 + ^2_2 = 1 + 9 = 10. Sum = 5 + 10 = 15.

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Trigonometry

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The value of $\sec^2(\tan^{-1}2) + cosec^2(\cot^{-1}3)$ is:

✅ Correct Option: 4

Let $\theta_1 = \tan^{-1}2$ , so $\tan\theta_1 = 2$ . Then $\sec^2\theta_1 = 1 + \tan^2\theta_1 = 1 + 4 = 5$ .

Let $\theta_2 = \cot^{-1}3$ , so $\cot\theta_2 = 3$ . Then $cosec^2\theta_2 = 1 + \cot^2\theta_2 = 1 + 9 = 10$ .

Sum $= 5 + 10 = 15$ .

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The value of sec⁡2(tan⁡−12)+cosec2(cot⁡−13)\sec^2(\tan^{-1}2) + cosec^2(\cot^{-1}3)sec2(tan−12)+cosec2(cot−13) is:

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CUET Mathematics Past Year Questions (Topic-Wise)

The value of $\sec^2(\tan^{-1}2) + cosec^2(\cot^{-1}3)$ is: