Question

if secA+tanA=p show that sinA=p²-1/p²+1​

Answer 1

Answer:

secA+tanA=p

----------------------------(1)

We know that,

sec²A-tan²A=1

or, (secA+tanA)(secA-tanA)=1

or, p(secA-tanA)=1

or, secA-tanA=1/p

-----------------------(2)

Adding (1) and (2) we get,

2secA=p+1/p

or, 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

Step-by-step explanation: