1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XI
Mathematics
L'Hospital Rule to Remove Indeterminate Form
Prove the fol...
Question
Prove the following:
s
i
n
x
+
s
i
n
3
x
c
o
s
x
+
c
o
s
3
x
=
t
a
n
2
x
Open in App
Solution
L
H
S
=
s
i
n
x
+
s
i
n
3
x
c
o
s
x
+
c
o
s
3
x
=
−
2
sin
(
x
+
3
x
2
)
cos
(
x
−
3
x
2
)
2
cos
(
x
+
3
x
2
)
cos
(
x
−
3
x
2
)
=
tan
2
x
=
R
H
S
Hence, proved
Suggest Corrections
0
Similar questions
Q.
Prove that
s
i
n
x
+
s
i
n
y
=
2
s
i
n
x
+
y
2
c
o
s
x
−
y
2
and hence show that
s
i
n
x
+
s
i
n
3
x
c
o
s
x
+
c
o
s
3
x
=
t
a
n
2
x
Q.
Prove that
cos
3
x
−
sin
3
x
cos
x
−
sin
x
=
1
2
(
2
+
sin
2
x
)
Q.
Solve the following equations:
(i)
cos
x
+
cos
2
x
+
cos
3
x
=
0
(ii)
cos
x
+
cos
3
x
-
cos
2
x
=
0
(iii)
sin
x
+
sin
5
x
=
sin
3
x
(iv)
cos
x
cos
2
x
cos
3
x
=
1
4
(v)
cos
x
+
sin
x
=
cos
2
x
+
sin
2
x
(vi)
sin
x
+
sin
2
x
+
sin
3
=
0
(vii)
sin
x
+
sin
2
x
+
sin
3
x
+
sin
4
x
=
0
(viii)
sin
3
x
-
sin
x
=
4
cos
2
x
-
2
(ix)
sin
2
x
-
sin
4
x
+
sin
6
x
=
0
Q.
Solve the following equations.
sin
x
+
sin
2
x
+
sin
3
x
=
cos
x
+
cos
2
x
+
cos
3
x
.
Q.
Evaluate:
sin
3
x
1
+
cos
x
+
cos
3
x
1
−
sin
x
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
L'hospitals Rule
MATHEMATICS
Watch in App
Explore more
NCERT - Standard XI
L'Hospital Rule to Remove Indeterminate Form
Standard XI Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app