Question

If tan theta=a/b then the value a sin theta + b cos thetha/ a sin theta - b cos theta​

Answer 1

Answer:

( a² + b² ) / ( a² - b² )

Step-by-step explanation:

Given---> tanθ = a / b

To find---> Value of

( aSinθ + bCosθ ) / ( aSinθ - bCosθ )

Solution---> ATQ, tanθ = a / b

Now,

( a Sinθ + bCosθ ) / ( aSinθ - bCosθ )

Taking , Cosθ , common from numerator and denominator , we get,

=Cosθ{a (Sinθ/Cosθ) + b} /Cosθ{a(Sinθ /Cosθ ) - b }

Cosθ , Cancel out from numerator and denominator and we get,

= {a ( Sinθ / Cosθ ) + b } / { a ( Sinθ / Cosθ ) - b }

= ( a tanθ + b ) / ( a tanθ - b )

Putting tanθ = a / b in it we get,

= {a ( a / b ) + b } / { a ( a / b ) - b }

= { ( a² /b ) + b } / { ( a ² / b ) - b }

Taking b , LCM in numerator and denominator, we get,

= { ( a² + b² ) / b } / { ( a² - b² ) / b }

= b ( a² + b² ) / b ( a² - b² )

b is cancel out from numerator and denominator,we get,

= ( a² + b² ) / ( a² - b² )

#Answerwithquality

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