Solved Example:
Prove:
cot A
–
cos A
cot A
+
cos A
=
cosec A – 1
cosec A + 1
Proof:
L.H.S
=
cot A
–
cos A
cot A
+
cos A
=
cos A
sin A
–
cos A
cos A
sin A
+
cos A
=
cos A
1
–
1
sin A
cos A
1
–
1
sin A
=
1
–
1
sin A
1
–
1
sin A
=
–
1
cosec A
+
1
cosec A
L.H.S = R.H.S
∴
∴
cot A
–
cos A
cot A
+
cos A
=
cosec A – 1
cosec A + 1
÷
÷
÷