If secA+tanA=p then show that psquarep-1÷psquare+1=simA

1.	If secA+tanA=p then show that psquarep-1÷psquare+1=simA
Answer» secA + tanA = p....................(1)We know that,sec²A - tan²A=1or, (secA + tanA)(secA-tanA)=1or, p(secA-tanA)=1or, secA-tanA=1/p .............(2)Adding (1) and (2) we get,2secA=p+1/por, secA=(p²+1)/2p∴, cosA=1/secA=2p/(p²+1)∴, sinA=√(1-cos²A)=√{1-4p²/(p²+1)²=√{(p²+1)²-4p²}/(p²+1)²=√(p⁴+2p²+1-4p²)/(p²+1)=√(p²-1)²/(p²+1)=(p²-1)/(p²+1) (Proved)

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