Question

If Cot theta + cosec theta=1.5 show that cos theta=5/13

Answer 1

Let @=theta
Cot@+Cosec@=3/2.............(i)
Multiply both sides by Cosec@-Cot@
Then,
Cosec²@-Cot²@=3/2(Cosec@-Cot@)
Since
Cosec²@-Cot²@=1
Hence,
Cosec@-Cot@=2/3.............(ii)
Add (i)+(ii)
2Cosec@=3/2+2/3= 13/6
Cosec@=13/12
Sin@=12/13
Hence,
Cos@=5/13
proved