MHT CET · Maths · Inverse Trigonometric Functions
The value of \(\tan ^2\left(\sec ^{-1} 4\right)+\cot ^2\left(\operatorname{cosec}^{-1} 3\right)\) is
- A 15
- B 25
- C 23
- D 7
Answer & Solution
Correct Answer
(C) 23
Step-by-step Solution
Detailed explanation
\(\tan ^2\left(\sec ^{-1} 4\right) = \sec ^2\left(\sec ^{-1} 4\right)-1 = 4^2-1 = 16-1 = 15\) \(\cot ^2\left(\operatorname{cosec}^{-1} 3\right) = \operatorname{cosec}^2\left(\operatorname{cosec}^{-1} 3\right)-1 = 3^2-1 = 9-1 = 8\)
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