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Prove the following: sinx- sinycosx+cosy=tan x-y2 - Mathematics

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Question

Prove the following:

`(sin x -  siny)/(cos x + cos y)= tan  (x -y)/2`

Sum

Solution

We have, बायाँ पक्ष = `(sin x -  siny)/(cos x + cos y)`

= `(2sin ((x - y )/2) cos ((x + y)/2))/(2cos ((x - y)/2) cos ((x + y)/2)`

= `(sin (x -y)/2)/(cos (x - y)/2)` 

= tan `(x - y)/2` = दायाँ पक्ष।

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Chapter 3: Trigonometric Functions - Exercise 3.3 [Page 73]

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NCERT Mathematics [English] Class 11
Chapter 3 Trigonometric Functions
Exercise 3.3 | Q 18 | Page 73

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