If sec θ + tan θ = p , then show that sin θ= p²-1/p²+1
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sec^2-tan^2=1 let teta be x
given
secx+tanx=p...................(1)
(secx+tanx)(secx-tanx)=1
p(secx-tanx)=1
secx-tanx=1/p...................(2)
add eq(1) and eq(2)
we will get
secx=p^2+1/p
subtract eq(1) and eq(2)
we will get
tanx=p^2-1/p
we know that
tanx/secx=sinx
then
p^2-1/p/p^2+1/p=sinx
therefore
p^2-1/p^2+1=sinx
hence proved
given
secx+tanx=p...................(1)
(secx+tanx)(secx-tanx)=1
p(secx-tanx)=1
secx-tanx=1/p...................(2)
add eq(1) and eq(2)
we will get
secx=p^2+1/p
subtract eq(1) and eq(2)
we will get
tanx=p^2-1/p
we know that
tanx/secx=sinx
then
p^2-1/p/p^2+1/p=sinx
therefore
p^2-1/p^2+1=sinx
hence proved
shadabaalam:
While adding (1) & (2), the result becomes 2secx=(p^2+1)/p; anyways it doesn't affect the solution.
in the place of /p write /2p
im telling u bcause i cant edit it now
yes yes, i already did that, i only wrote it to let know to others, who copy and paste the solution..
huh copy and paste where
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