Question

prove tha t Tan^2 A / (SecA-1)^2 = ( cosecA + cotA)^2​

Answer 1

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tan²A / ( secA - 1 )² = ( cosecA + cotA)²

Taking L. H. S

= ( tanA / secA - 1 )²

= we know,

tan ¤ = sin¤ / cos¤ and

sec¤ = 1 / cos¤

= ( ( sinA / cosA ) / ( 1 / cosA ) - 1 )²

= ( sin A / cosA / ( 1 - cosA ) / cosA )²

= ( sinA / 1 - cosA)²

Rationalising the denominator

= ( sinA ( 1 - cosA ) / 1 - cos²A)²

= we know,

sin²¤ = 1 - cos²¤

= ( sinA ( 1 - cosA ) / sin²A )²

= ( 1 - cosA / sinA)²

= ( cosecA - cotA )²

Hence L. H. S = R. H. S

Hence proved.

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