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in the following trigonometry expression find the
Question:
In the following trigonometry expression, find the value of (MN).
(
1
+
cos
x
)
(
1
−
sin
x
)
(
sin
x
+
cos
x
−
1
)
2
=
M
sin
N
x
MHT CET
Updated On:
May 1, 2024
(A) 3
(B) 6
(C) 4
(D) 2
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The Correct Option is
C
Solution and Explanation
Explanation:
Given:
(
1
+
cos
x
)
(
1
−
sin
x
)
(
sin
x
+
cos
x
−
1
)
2
=
M
sin
N
x
Formula:
(
sin
x
+
cos
x
−
1
)
2
=
2
(
1
−
sin
x
)
(
1
−
cos
x
)
According to the question:
⇒
(
1
+
cos
x
)
(
1
−
sin
x
)
×
2
(
1
−
sin
x
)
(
1
−
cos
x
)
=
M
sin
N
x
⇒
2
(
1
+
cos
x
)
(
1
−
cos
x
)
=
Msin
N
x
⇒
2
(
1
−
cos
2
x
)
=
M
sin
N
x
⇒
2
sin
2
x
=
M
sin
N
x
Comparing both sides, we have
⇒
MN
=
(
2
×
2
)
=
4
Hence, the correct option is (C).
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