Math, asked by wiolla, 1 year ago

can anyone solve this

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Answered by hari479
0

I don't know trignomentary.......so pls forgive me

Answered by BraɪnlyRoмan
7

 \huge \boxed{ \bf{question}}

PROVE THAT :

1> Sec A (1-SinA) (SecA+TanA) = 1

2> Cosec A (1+CosA) (CosecA-Cot) = 1

 \huge \boxed{ \bf{answer}}

1>> Sec A (1-SinA) (SecA+TanA) = 1

LHS,

 = secA(1 - sinA)(secA + tanA)

 = \frac{1}{ \cos A} (1 - sinA)( \frac{1}{cosA} + \frac{sinA}{cos A })

 = ( \frac{1}{cos A } - \frac{sin A }{cos A } )( \frac{1} {cos A } + \frac{sinA} {cos A })

 = (\frac{1 - sin A }{cos A} )( \frac{1 + sin A }{cos A} )

 = \frac{1 - {cos \: }^{2} A }{ {cos}^{2} A }

 = \frac{ {cos }^{2}A }{ {cos }^{2} A}

 = 1

= RHS

2>> Cosec A (1+CosA) (CosecA-Cot) = 1

LHS,

 = cosecA(1 + cosA)(cosecA - cot A)

 = \frac{1}{sin A }(1 + cosA)( \frac{1}{sinA } - \frac{cos A}{sin A} )

 = ( \frac{1}{sin A} + \frac{cos A}{sin A } )( \frac{1}{sin A } - \frac{cos A}{sin A } )

 = (\frac{1 + cos A }{sinA } )( \frac{1 - cos A }{sin A} )

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

 = \frac{ {sin \: }^{2} A }{ {sin}^{2} A}

 = 1

= RHS

Hence , Proved.

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