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

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प्रश्न

Prove the following:

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

योग
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उत्तर

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

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

= sin x cos x [tanx + cot x]

= sin x cos x `[(sinx + cos x)/(cos x + sin x)]`

= sin x cos x `(1/(sinx cosx))=1`

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अध्याय 3: Trigonometric Functions - Exercise 3.3 [पृष्ठ ७३]

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एनसीईआरटी Mathematics [English] Class 11
अध्याय 3 Trigonometric Functions
Exercise 3.3 | Q 9 | पृष्ठ ७३

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