Grade 10Trigonometry
Cosec÷cosec-1+cosec÷Cosec+1 prove that this question answer
1 Answer
Arun
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
= [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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