Math, asked by kalia4449, 1 year ago

(cosecA -sinA) (secA-cosA)=1\tanA+cotA

Answers

Answered by kishorkunal050
13

Step-by-step explanation:

detailed explanation is shown above

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Answered by aquialaska
12

Answer:

To  Prove: (cosec\,A-sin\,A)(sec\,A-cos\,A)=\frac{1}{tan\,A+cot\,A}

Consider,

LHS = ( cosec A - sin A )( sec A - cos A )

       = ( 1/sin A - sin A )( 1/cos A - cos A )

       =(\frac{1-sin^2\,A}{sin\,A})(\frac{1-cos^2\,A}{cos\,A})

       =(\frac{cos^2\,A}{sin\,A})(\frac{sin^2\,A}{cos\,A})

       =cos\,A\:\:sin\,A

RHS = \frac{1}{tan\,A+cot\,A}

       =\frac{1}{\frac{sin\,A}{cos\,A}+\frac{cos\,A}{sin\,A}}

       =\frac{1}{\frac{sin^2\,A+cos^\,A}{cos\,A\:\:sin\,A}}

       =\frac{cos\,A\:\:sin\,A}{sin^2\,A+cos^2\,A}

       =\frac{cos\,A\:\:sin\,A}{1}

       =cos\,A\:\:sin\,A

LHS = RHS

Hence Proved.

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