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Mathematics
Mathematics
Problem
27. a. Prove that:
tan
θ
1
−
cot
θ
+
cot
θ
1
−
tan
θ
=
1
+
sec
θ
csc
θ
\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \sec \theta \csc \theta
1
−
c
o
t
θ
t
a
n
θ
+
1
−
t
a
n
θ
c
o
t
θ
=
1
+
sec
θ
csc
θ
b. OR Prove that:
sin
A
+
cos
A
sin
A
−
cos
A
+
sin
A
−
cos
A
sin
A
+
cos
A
=
2
2
sin
2
A
−
1
\frac{\sin A + \cos A}{\sin A - \cos A} + \frac{\sin A - \cos A}{\sin A + \cos A} = \frac{2}{2 \sin^2 A - 1}
s
i
n
A
−
c
o
s
A
s
i
n
A
+
c
o
s
A
+
s
i
n
A
+
c
o
s
A
s
i
n
A
−
c
o
s
A
=
2
s
i
n
2
A
−
1
2
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