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Evaluate: `Sec{Cot^-1(-5/12)}` - Mathematics

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Question

Evaluate:

`sec{cot^-1(-5/12)}`

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Solution

`sec{cot^-1(-5/12)}=sec{pi-cot^-1(5/12)}`

`=-sec{cot^-1(5/12)}`

`=-sec{cos^-1[1/(1+(12/5)^2)]}`

`=-sec{cos^-1(5/13)}`

`=-sec{sec^-1
(13/5)}`

`=-13/5`

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Chapter 4: Inverse Trigonometric Functions - Exercise 4.09 [Page 58]

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RD Sharma Mathematics [English] Class 12
Chapter 4 Inverse Trigonometric Functions
Exercise 4.09 | Q 1.2 | Page 58

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