If seco + tan 0=p, then what is the value of seco - tan 0 ?
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Step-by-step explanation:
secθ+tanθ=P
⇒(secθ+tanθ)
2
=P
2
⇒sec
2
θ+tan
2
θ+2tanθsecθ=P
2
⇒2tan
2
θ+1+
cosθ
2sinθ
=P
2
⇒
cos
2
θ
2sin
2
θ+cos
2
θ+2sinθ
=P
2
Applying componendo and dividendo
2sin
2
θ+cos
2
θ+2sinθ−cos
2
θ
2sin
2
θ+cos
2
θ+2sinθ−cos
2
θ
=
P
2
+1
P
2
−1
⇒
2(sinθ+1)
2sinθ(sinθ+1)
=
P
2
+1
P
2
−1
⇒sinθ=
P
2
+1
P
2
−1
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