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If sec + tan = p.
Then find the value of cosec.
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Secondary SchoolMath 8+4 pts
If sec theta + tan theta = p, then find the value of cosec theta
by Imhanmerincess 18.08.2016
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ARoy
ARoy ★ Brainly Teacher ★
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) Ans.
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________Heyy Buddy ❤_______
_____Here's your Answer ________
Given;
Sec + tan = p. ---------------(1)
We know that,
Sec^2 theta - tan^2 theta = 1.
=> (sec - tan)(sec + tan) = 1.
=> sec - tan = 1/p -----------(2)
=> Adding eq 1 and 2, we get
=> ( sec - tan) + (Sec + tan) = p + 1/p
=> 2 sec = ( p^2 + 1) / p
=> sec = (p^2 + 1) / 2p.
=> It can be written as cosθ = 1/secθ = 2p/(p²+1)
OR 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)
✔✔✔
_____Here's your Answer ________
Given;
Sec + tan = p. ---------------(1)
We know that,
Sec^2 theta - tan^2 theta = 1.
=> (sec - tan)(sec + tan) = 1.
=> sec - tan = 1/p -----------(2)
=> Adding eq 1 and 2, we get
=> ( sec - tan) + (Sec + tan) = p + 1/p
=> 2 sec = ( p^2 + 1) / p
=> sec = (p^2 + 1) / 2p.
=> It can be written as cosθ = 1/secθ = 2p/(p²+1)
OR 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)
✔✔✔
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