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Byju's Answer
Standard XII
Mathematics
Trigonometric Equations
If sin x+co...
Question
If
sin
x
+
cos
x
sin
x
−
cos
x
+
sin
x
−
cos
x
sin
x
+
cos
x
=
m
sec
2
x
tan
2
x
−
1
. Find
m
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Solution
Consider
L
H
S
=
(
sin
x
+
cos
x
)
2
+
(
sin
x
−
cos
x
)
2
(
sin
x
−
cos
x
)
(
sin
x
+
cos
x
)
=
sin
2
x
+
cos
2
x
+
2
sin
x
cos
x
+
sin
2
x
+
cos
2
x
−
2
sin
x
cos
x
sin
2
x
−
cos
2
x
=
2
(
sin
2
x
+
cos
2
x
)
sin
2
x
−
cos
2
x
=
2
sin
2
x
−
cos
2
x
⟶
(
1
)
Now consider
R
H
S
=
m
(
1
cos
2
x
)
sin
2
x
cos
2
x
−
1
=
m
sin
2
x
−
cos
2
x
⟶
(
2
)
Equating (1) & (2)
m
=
2
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Similar questions
Q.
Prove :
1
+
cos
x
+
sin
x
1
+
cos
x
−
sin
x
=
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If
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