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+6 votes
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in Mathematics by (347 points)
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If sec θ + tan θ = p, find the value of cosec θ.

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+6 votes
by (347 points)
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This is correct

by (12 points)
+1
What is D
by (347 points)
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D=b²-4ac (Discriminant)
+2 votes
by (65.3k points)

Secθ+tanθ=p ----------------------(1)

∵, sec²θ-tan²θ=1

or, (secθ+tanθ)(secθ-tanθ)=1

or, secθ-tanθ=1/p ----------------(2)

Adding (1) and (2) we get,

2secθ=p+1/p

or, secθ=(p²+1)/2p

∴, cosθ=1/secθ=2p/(p²+1)

∴, sinθ=√(1-cos²θ)

=√[1-{2p/(p²+1)}²]

=√[1-4p²/(p²+1)²]

=√[{(p²+1)²-4p²}/(p²+1)²]

=√[(p⁴+2p²+1-4p²)/(p²+1)²]

=√(p⁴-2p²+1)/(p²+1)

=√(p²-1)²/(p²+1)

=(p²-1)/(p²+1)

∴, cosecθ=1/sinθ=1/[(p²-1)/(p²+1)]=(p²+1)/(p²-1) 

+2 votes
by (79.6k points)

Given,

 sec θ + tan θ = p

Converting sec θ and tan θ in sin θ and cos θ

So, we square both sides

+2 votes
by (7.2k points)

simply we can solve it by:

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