is sin P= then find tan theta cos theta values
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Answer:
We have sec
2
θ−tan
2
θ=1
(secθ−tanθ)(secθ+tanθ)=1
(secθ−tanθ)p=1 (∵secθ+tanθ=p)
(secθ−tanθ)=
p
1
secθ+tanθ=p
secθ−tanθ=
p
1
2secθ=
p
p
2
+1
secθ=
2p
p
2
+1
cosθ=
p
2
+1
2p
sinθ=
1−cos
2
θ
cos
2
θ=(
p
2
+1
2p
)
2
cos
2
θ=
p
4
+1+2p
2
4p
2
1−cos
2
θ=1−
p
4
+1+2p
2
4p
2
=
(p
2
+1)
2
p
4
+1+2p
2
−4p
2
=
(p
2
+1)
2
p
4
+1−2p
2
=
(p
2
+1)
2
(p
2
−1)
2
1−cos
2
θ
=
p
2
+1
p
2
−1
∴sinθ=
p
2
+1
p
2
−1
∴cosec θ=
sinθ
1
=
p
2
−1
p
2
+1
Step-by-step explanation:
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