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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Coscoscos-1(cos7π6) = _________. - Mathematics and Statistics

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प्रश्न

`"cos"^-1 ("cos" (7pi)/6)` = _________.

पर्याय

  • `(7pi)/6`

  • `(5pi)/6`

  • `pi/6`

  • `(3pi)/2`

MCQ
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उत्तर

`"cos"^-1 ("cos" (7pi)/6) = (5pi)/6`.

Explanation:

You can write `(7pi)/6  as  (pi + pi/6)`

Thus, we can clearly see the angle falls in the third quadrant, and the cosine value in this quadrant is always negative.

Hence, `cos(pi + pi/6) = -cos(pi/6)`

coming back to the question

`cos^(-1)[cos((7pi)/6)] = cos^(-1)[-cos(pi/6)]`

= `pi - cos^(-1)[cos(pi/6)]`

= `pi - pi/6`

= `(5pi)/6`

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Trigonometric Equations and Their Solutions
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Trigonometric Functions - Miscellaneous exercise 3 [पृष्ठ १०७]

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बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
पाठ 3 Trigonometric Functions
Miscellaneous exercise 3 | Q 1.11 | पृष्ठ १०७

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