Question

If secA+tanA=P then show that p^2-1/p^2+1

Answer 1

heya friend ☺
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,Here is ur answer....
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SecA+TanA=P.--------1)

and ,by using rationalizing process

then 1/p=1/secA+tanA,*tanA-secA/secA-tanA

=>secA-tanA/sec^2 A-tan^2A

=>secA-tanA/1【since sec^2A-tan^2A】

=>secA-tanA...........1/p

now,,adding both equation ..

we get...

secA-tanA+secA,+tanA=1/p+p

2secA=p+p^2/p----------3)

and again....substraction 1 from 2

secA+tanA-(secA-tanA)=p-1/p

=>2tanA=p^2+p/p

=>2tanA=p^2+p/p-------4)

now ,
if we dividing both equation 3 to 4 we get ..

2secA/2tanAA=p^2-p/p/p^2+p/p

=>cosA=p^2-p/p^2+1 Ans...prooved

hope it helps you ☺

@Rajukumar☺☺