If secA+tan A=p Prove that sin A = psquare-1 divided by p square +1

1.	If secA+tan A=p Prove that sin A = psquare-1 divided by p square +1
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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