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Byju's Answer
Standard XII
Mathematics
Trigonometric Ratios of Compound Angles
If tan x=a b,...
Question
If
tan
x
=
a
b
,
show that
a
sin
x
-
b
cos
x
a
sin
x
+
b
cos
x
=
a
2
-
b
2
a
2
+
b
2
.
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Solution
LHS
:
a
sin
x
-
b
cos
x
a
sin
x
+
b
cos
x
Dividing
by
b
cos
x
:
=
a
tan
x
b
-
1
a
tan
x
b
+
1
Substituting
the
value
of
tan
x
=
a
2
-
b
2
a
2
+
b
2
=
RHS
Hence proved.
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3
Similar questions
Q.
If
sin
x
=
a
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-
b
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a
2
+
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2
, then the values of tan x, sec x and cosec x
Q.
If
tan
θ
=
a
b
,
show that
a
sin
θ
-
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cos
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α
sin
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=
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Q.
If
sin
x
+
sin
y
=
a
and
cos
x
+
cos
y
=
b
show that
tan
(
x
−
y
2
)
=
±
√
(
4
−
a
2
−
b
2
a
2
+
b
2
)
Q.
If θ =
a
b
, then
(
a
sinθ
-
b
cosθ
)
(
a
sin
θ
+
b
cosθ
)
= ?
(a)
(
a
2
+
b
2
)
(
a
2
-
b
2
)
(b)
(
a
2
-
b
2
)
(
a
2
+
b
2
)
(c)
a
2
(
a
2
+
b
2
)
(d)
b
2
(
a
2
+
b
2
)
Q.
Prove that:
(
a
2
+
b
2
)
(
a
2
+
b
2
)
−
(
a
2
−
b
2
)
(
a
2
−
b
2
)
=
4
a
2
b
2
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