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Prove the following: cosec(90∘-x)sin(180∘-x)cot(360∘-x)sec(180∘+x)tan(90∘+x)sin(-x) = 1

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Question

Prove the following:

`("cosec"(90^circ - x)sin(180^circ - x)cot(360^circ - x))/(sec(180^circ + x)tan(90^circ + x)sin(-x))` = 1

Sum
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Solution

L.H.S. = `("cosec"(90^circ - x)sin(180^circ - x)cot(360^circ - x))/(sec(180^circ + x)tan(90^circ + x)sin(-x))`

= `(secx*sinx*(- cotx))/((-secx)*(-cotx)*(- sinx)`

= `(secx*sinx*cotx)/(secx*cotx*sinx)`

= 1

= R.H.S.

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Chapter 3: Trigonometry - 2 - Exercise 3.2 [Page 42]

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