If secθ + tanθ = p, then find the value of cosecθ ??

1.	If secθ + tanθ = p, then find the value of cosecθ ??
Answer» Given, sec θ + tan θ = p ...........1We know that sec2\xa0θ\xa0- tan2\xa0θ =\xa01=> (sec θ\xa0- tan θ)(sec θ + tan θ) = 1=>\xa0(sec θ\xa0- tan θ) * p = 1=>\xa0sec θ\xa0- tan θ = 1/p ............2Add equation 1 and 2, we get 2 * sec θ = p + 1/p=>\xa02 * sec θ = (p2\xa0+ 1)/p=>\xa0sec θ = (p2\xa0+ 1)/2pand\xa0cos θ = 1/sec θ=>\xa0cos θ = 2p/(p2\xa0+ 1)Subtract equation 1 and 2, we get 2 \xa0tan θ = p\xa0- 1/p=>\xa02 \xa0tan θ = (p2\xa0- 1)/p=>\xa0tan θ = (p2\xa0- 1)/2pand\xa0cot θ = 1/tan θ=>\xa0cot θ = 2p/(p2\xa0- 1)We know that tan θ =\xa0sin θ/ cos θ=>\xa0sin θ =\xa0tan θ \xa0cos θ=>\xa0sin θ =\xa0{(p2\xa0- 1)/2p} \xa0{2p/(p2\xa0+ 1)}=>\xa0sin θ = (p2\xa0- 1)/(p2\xa0+ 1)and\xa0cosec θ = 1/sin\xa0θ\xa0=> cosec θ = (p2\xa0+ 1)/(p2\xa0- 1)\xa0

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