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Tamil Nadu Board of Secondary EducationHSC Science Class 12

Find the value of cos-1[cos π7cos π17-sin π7sin π17] - Mathematics

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Question

Find the value of `cos-1 [cos  pi/7 cos  pi/17 - sin  pi/7 sin  pi/17]`

Sum

Solution

`cos-1 [cos  pi/7 cos  pi/17 - sin  pi/7 sin  pi/17]`

= `cos^1[cos(pi/7 + pi/17)]`

∵ cos(A + B) = cos A cos B – sinA sin B

= `cos1 [cos((17pi + 7pi)/119)]`

= `cos^1[cos((24pi)/119)]`

= `(24pi)/119`

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The Cosine Function and Inverse Cosine Function
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Chapter 4: Inverse Trigonometric Functions - Exercise 4.2 [Page 142]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 12 TN Board
Chapter 4 Inverse Trigonometric Functions
Exercise 4.2 | Q 5. (iii) | Page 142
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