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(Sin A)/(1 + Cos A) + (1 + Cos A)/(Sin A) = 2 Cosec a - Mathematics

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Sum

`(sin A)/(1 + cos A) + (1 + cos A)/(sin A)` = 2 cosec A

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Solution

LHS = `((sin^2 A + ( 1 + cos A)^2)/((1 + cos A)sin A))`

= `(sin^2 A + 1 + cos^2 A + 2 cos A)/((1 + cos A) sin A)`

= `(1 + 1 + 2 cos A)/((1 + cos A) sin A)`

= `(2(1 + cos A))/((1 + cos A)sin A)`

= 2 cosec A
= RHS
Hence proved.

Concept: Trigonometric Identities
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APPEARS IN

ICSE Class 10 Mathematics
Chapter 18 Trigonometry
Exercise | Q 7
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