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InterviewSolution
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If secA+tanA=p, then find the value of cosecA |
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Answer» Arrange krlena ache se smjhke bnana secA+tanA=p ----------- (i)‘.\' sec²A-tan²A=1(secA+tanA)(secA-tanA)=1secA-tanA = 1/p ------------- (ii)Subtracting eqn ii from IWe get,2tanA= p-1/ptanA = (p²-1)/2pcotA = 2p/(p²-1)Nowcosec²A-cot²A = 1cosec²A=1+cot²Acosec²A=1+[2p/(p²-1)]²cosec²A= 1+4p²/(p²-1)²cosec²A= (p²)² - 2p²- 1- 4p²/(p²-1)²cosec²A= (p²)² + 2p²+1/(p²-1)²cosec²A= (p²+1)² / (p²-1)²cosecA= (p²+1)/p²-1) secA+tanA=p ----------------------------(1)∵, sec²A-tan²A=1or, (secA+tanA)(secA-tanA)=1or, secA-tanA=1/p -----------------------(2)Subtracting (2) from (1) we get,2tanA=p-1/por, tanA=(p²-1)/2p∴, cotA=2p/(p²-1)Now, cosec²A-cot²A=1or, cosec²A=1+cot²Aor, cosec²A=1+{2p/(p²-1)}²or, cosec²A=1+4p²/(p²-1)²or, cosec²A=(p⁴-2p²+1+4p²)/(p²-1)²or, cosec²A=(p⁴+2p²+1)/(p²-1)²or, cosec²A=(p²+1)²/(p²-1)²or, cosecA=(p²+1)/(p²-1) |
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