prove that sin ( theta + phy )/sin theta × cos phy = cot theta × tan phy + 1 .
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Answer:
We need
sin
(
a
+
b
)
=
sin
a
cos
b
+
sin
b
cos
a
cos
(
a
−
b
)
=
cos
a
cos
b
+
sin
a
sin
b
Therefore,
L
H
S
=
sin
(
θ
+
ϕ
)
cos
(
θ
−
ϕ
)
=
sin
θ
cos
ϕ
+
cos
θ
sin
ϕ
cos
θ
cos
ϕ
+
sin
θ
sin
ϕ
Dividing by all the terms by
cos
θ
cos
ϕ
=
sin
θ
cos
ϕ
cos
θ
cos
ϕ
+
cos
θ
sin
ϕ
cos
θ
cos
ϕ
cos
θ
cos
ϕ
cos
θ
cos
ϕ
+
sin
θ
sin
ϕ
cos
θ
cos
ϕ
=
sin
θ
cos
θ
+
sin
ϕ
cos
ϕ
1
+
sin
θ
cos
θ
⋅
sin
ϕ
cos
ϕ
=
tan
θ
+
tan
ϕ
1
+
tan
θ
tan
ϕ
=
R
H
S
Q
E
D
Step-by-step explanation:
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