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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Select the correct option from the given alternatives: "tan"(2"tan"^-1 (1/5) - pi/4) = ______

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प्रश्न

Select the correct option from the given alternatives:

`"tan"(2"tan"^-1 (1/5) - pi/4)` = ______

पर्याय

  • `17/7`

  • `-17/7`

  • `7/17`

  • `-7/17`

MCQ
रिकाम्या जागा भरा
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उत्तर

`"tan"(2"tan"^-1 (1/5) - pi/4) = \underline(-7/17)`.

Explanation:

`tantheta = 1/5`

`tan(2theta) = (2tantheta)/(1-tan^2theta)`

`tan(2theta) = 2(1/5)/1-(1/5)^2 = (2/5)/(1-1/25) = (2/5)/(24/25) = 2/5 xx 25/24 = 50/120 = 5/12`

`tan(2theta) = 5/12`

`tan(2theta-pi/4) = (tan(2theta)-tan  pi/4)/(1+tan(2theta)tan  pi/4)`

`tan(2theta - pi/4) = (5/12 -1)/(1+5/12 xx 1) = ((5-12)/12)/(1+5/12) = (-7/12)/(17/12) = -7/17`

`=-7/17`

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पाठ 3: Trigonometric Functions - Miscellaneous exercise 3 [पृष्ठ १०८]

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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 1.16 | पृष्ठ १०८

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