Question

Prove that 1+ Cos^2 A/Cosec A=Cosec A
(Cosec A is only the denominator of Cos^2 A, 1 has no denominator)

Answer 1

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Secondary School

Math

5+3 pts

Cosec A - 1/ cosec A + 1 = ( cos A / 1 + sin A)^2

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 by Pranav3910 19.03.2018

Answers





ShivaniK123 

Virtuoso

cosec A - 1 = (1/sinA) -1
= (1-sinA) / sinA

cosec A + 1 = (1/sinA) +1
= (1+sinA) / sinA

Now, (cosec A - 1) / (cosec A + 1) = 
[ (1-sinA) / sinA ] / [ (1+sinA) / sinA ]
= [ (1-sinA) / sinA ] x [ sinA / (1+sinA) ]
= 1-sinA / 1+sinA
Now multiplying numerator and denominator by 1+sinA we get 
= ( 1-sinA )x( 1+sinA ) / ( 1+sinA )²
= (1-sin²A) / ( 1+sinA )²

But ,
cos²A+ sin²A =1
cos²A = 1 - sin²A
So now substituting this value of 1 - sin²A
cosec A - 1 / cosec A + 1 = cos²A / ( 1+sinA )²
=RHS

Hence proved