Question

cotA - tanA -- 2 tan 2A - 4tan 4A
2. 2 A​

Answer 1

Answer:

As cotA−tanA=  

sinA

cosA

​  

−  

cosA

sinA

​  

=  

sinAcosA

cos  

2

A−sin  

2

A

​  

=2cot2A

⇒tanA=cotA−2cot2A

Our expression L.H.S becomes

cotA−2cot2A+2tan2A+4tan4A+8cot8A

=cotA−2(cot2A−tan2A)+4tan4A+8cot8A

=cotA−2(2cot4A)+4tan4A+8cot8A

=cotA−4(cot4A−tan4A)+8cot8A

=cotA−8cot8A+8cot8A

=cotA⇒k=1