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