20
(1-sin cos ) 3
If tan 0= then prove that
21
(1+ sin 0+ cos 0) 7
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Answer:
tanθ=
21
20
As 1+tan
2
θ=sec
2
θ
1+
21×21
20×20
=sec
2
θ
1+
441
400
=sec
2
θ
441
841
=sec
2
θ
secθ=
21
29
cosθ=
29
21
(1)
As 1=cos
2
θ+sin
2
θ
1=
29×29
21×21
+sin
2
θ
1=
841
441
+sin
2
θ
1−
841
441
=sin
2
θ
841
400
=sin
2
θ
29
20
=sinθ (2)
1+sinθ+cosθ
1−sinθ+cosθ
(3)
Substituting (1) and (2) in (3)
1+
29
20
+
29
21
1−
29
20
+
29
21
=
1+
29
41
1+
29
1
=
29
70
29
30
=
70
30
=
7
3
LHS=RHS
Hence proved.
Step-by-step explanation:
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