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Question

If secx+tanx=p, then which of the following is/are correct?

A
sinx=p21p2+1
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B
cosx=2pp2+1
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C
tanx=p212p
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D
secx=p2+12p
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Solution

The correct options are
A sinx=p21p2+1
B cosx=2pp2+1
C tanx=p212p
D secx=p2+12p
secx+tanx=p(1)
We know that,
sec2xtan2x=1secxtanx=1secx+tanxsecxtanx=1p(2)
From equation (1) and (2),
2secx=p+1psecx=p2+12pcosx=2pp2+1
And
2tanx=p1ptanx=p212p
Now,
sinx=tanx×cosx=p21p2+1

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