Question

(sin X +sin y)(sin X -sin y)/(cos y+cos X) (cos y -cos X)=???
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Answer 1

Answer:

- [ sin{ ( X - Y ) / 2 } ] / [ sin{ ( Y - X ) / 2 ]

Step-by-step-explanation:

Given equation : [ ( sinX + sinY )( sinX - sinY ) / ( cosX + cosY )( cosY - cosX ) ]

From the properties of trigonometric ratios :

sinA + sinB = 2sin{ ( A + B ) / 2 }cos{ ( A - B )/ 2 }

sinA - sinB = 2cos{ ( A + B ) / 2 }sin{ ( A - B ) / 2 }

cosA + cosB = 2cos{ ( A + B ) / 2 } cos{ ( A - B ) / 2 }

cosA - cosB = - 2sin{ ( A + B ) / 2 } sin{ ( B - A ) / 2 }

By using the properties given above :

= > [ 2sin{ ( sinX + Y ) / 2 }cos{ ( X - Y )/ 2 } x 2cos{ ( X + Y ) / 2 }sin{ ( X - Y ) / 2 } ] / [ 2cos{ ( X + Y ) / 2 } cos{ ( X - Y ) / 2 } x - 2sin{ ( X + Y ) / 2 } sin{ ( Y - X ) / 2 } ]

= > - [ sin{ ( X - Y ) / 2 } ] / [ sin{ ( Y - X ) / 2 ]

Hence the required value is - [ sin{ ( X - Y ) / 2 } ] / [ sin{ ( Y - X ) / 2 ]

Answer 2

Step-by-step explanation:

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