Question

If sec theta +tan theta =p ,find the value of tan theta in terms of p

Answer 1

secϴ+tanϴ=p

according to the identity,

sec²ϴ-tan²ϴ=1

(secϴ+tanϴ)(secϴ-tanϴ)=1

secϴ-tanϴ=1/p

add two equations,

secϴ+tanϴ+secϴ-tanϴ=p+1/p

2secϴ=p²+1

secϴ=(p²+1)/2

substitute in equation 1

secϴ+tanϴ=p

tanϴ=p-(p²+1)/2

=(2p-p²-1/)2

=-(p-1)²/2