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Byju's Answer
Standard XII
Mathematics
Sin2A and Cos2A in Terms of tanA
Let x, y be r...
Question
Let
x
,
y
be real numbers such that
x
cos
2
39
∘
=
tan
26
∘
cot
39
∘
tan
86
∘
cos
78
∘
tan
34
∘
and
y
cos
81
∘
=
cos
36
∘
−
sin
36
∘
.
Then the value of
x
+
y
2
is
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Solution
x
=
(
tan
26
∘
tan
86
∘
tan
34
∘
)
cos
39
∘
cos
78
∘
sin
39
∘
cos
2
39
∘
We know
tan
x
tan
(
60
∘
−
x
)
tan
(
60
∘
+
x
)
=
tan
3
x
∴
x
=
2
tan
78
∘
cos
78
∘
2
sin
39
∘
cos
39
∘
=
2
tan
78
∘
tan
78
∘
=
2
y
cos
81
∘
=
√
2
√
2
(
cos
36
∘
−
sin
36
∘
)
=
√
2
sin
(
45
∘
−
36
∘
)
=
√
2
sin
9
∘
=
√
2
cos
81
∘
⇒
y
=
√
2
∴
x
+
y
2
=
4
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0
Similar questions
Q.
Let
x
,
y
be real numbers such that
x
cos
2
39
∘
=
tan
26
∘
cot
39
∘
tan
86
∘
cos
78
∘
tan
34
∘
and
y
cos
81
∘
=
cos
36
∘
−
sin
36
∘
.
Then the value of
x
+
y
2
is
Q.
Let
x
,
y
,
z
and
r
be positive real numbers such that
x
2
+
y
2
+
z
2
=
r
2
.
Then the value of
tan
−
1
(
x
y
z
r
)
+
tan
−
1
(
y
z
x
r
)
+
tan
(
z
x
y
r
)
is
Q.
Let x and y be two real numbers such that x > 0 and xy
=
1.
The minimum value of x+y is
Q.
Let
x
and
y
be two positive real numbers such that
x
y
=
1.
The minimum value of
x
+
y
is
Q.
lf x, y are two real numbers such that
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y
2
=
1
, then the maximum value of x+y is
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Sin2A and Cos2A in Terms of tanA
Standard XII Mathematics
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