prove that (tan A + cosec B) ^2 -(cot B - sec A) ^2= 2 tan A*cot B (cosec A - sec B)
Answers
Answered by
8
LHS = (tanA - cosecB)² - (cotB - secA)²
= tan²A + cosec²B - 2tanA. cosecB - [cot²B + sec²A - 2cotB. secA ]
= (tan²A - sec²A) + (cosec²B - cot²B ) + 2tanA. cosecB + 2cotB. secA
= -1 + 1 - 2tanA. cosecB + 2cotB. secA
= 2cotB. secA - 2tanA. cosecB
= 2tanA. cotB [ secA/tanA - cosecB/cotB]
[ as we can see that, secA/tanA = cosecA and cosecB/cotB = secB ]
= 2tanA. cotB [ cosecA - secB ] = RHS
hence, proved
Similar questions