tan theta =2(x+1)/2x+1 find sin theta and cos theta in terms of x
Answers
Answered by
1
Answer:
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Step-by-step explanation:
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Answered by
1
Step-by-step explanation:
tanθ=
2x+1
2x(x+1)
,
sec
2
θ=1+tan
2
θ
=1+
(2x+1)
2
(2x(x+1))
2
=
(2x+1)
2
(2x+1)
2
+4x
2
(x+1)
2
=
(2x+1)
2
(2x
2
+2x+1)
2
and
secθ=
(2x+1)
(2x
2
+2x+1)
,
cosθ=
(2x
2
+2x+1)
(2x+1)
, We have
sin
2
θ=1−cos
2
θ
=1−(
(2x
2
+2x+1)
(2x+1)
)
2
=
(2x
2
+2x+1)
2
(2x
2
+2x+1)
2
−(2x+1)
2
using a
2
−b
2
=(a+b)(a−b)
=
(2x
2
+2x+1)
2
(x
2
+2x+1)(4x
2
)
and this gives sinθ=
(2x
2
+2x+1)
(x+1)(2x)
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