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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Prove the following: cos(3π2+x)cos(2π+x)[cot(3π2-x)+cot(2π+x)] = 1

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प्रश्न

Prove the following:

`cos((3pi)/2 + x) cos(2pi + x)[cot((3pi)/2 - x) + cot(2pi + x)]` = 1

बेरीज
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उत्तर

L.H.S. = `cos((3pi)/2 + x) cos(2pi + x)[cot((3pi)/2 - x) + cot(2pi + x)]`

= sin x · cos x [tan x + cot x]

= `sinx * cosx[sinx/cosx + cosx/sinx]`

= `sinx*cosx[(sin^2x + cos^2x)/(sinx*cosx)]`

= `sinx*cosx xx 1/(sinx*cosx)`

= 1

= R.H.S.

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पाठ 3: Trigonometry - 2 - Exercise 3.2 [पृष्ठ ४२]

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