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Cosec÷cosec-1+Cosec÷Cosec+1= 2sec×secprove that this question

Cosec÷cosec-1+Cosec÷Cosec+1= 2sec×secprove that this question

Grade:10

1 Answers

Arun
25763 Points
4 years ago
cscA /(cscA - 1 ) + cscA/(cscA + 1) 
= [cscA(cscA - 1) + cscA(cscA + 1)] / (cscA - 1)(cscA + 1) 
= cscA(cscA - 1 + cscA + 1) / (cscA - 1)(cscA + 1) 
= cscA( 2cscA ) / (csc²A - 1 ) 
= 2csc²A / csc²A - 1 
= 2/sin²A / (1/sin²A - 1 ) 
= 2/sin²A / (1 - sin²A )/sin²A 
= 2 / (1 - sin²A ) 
= 2 / cos²A 
= 2.sec²A

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