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If (tan3A)/(tanA)=k(k!=1) then which of ...

If `(tan3A)/(tanA)=k(k!=1)` then which of the following is not true? `(cosA)/(cos3A)=(k-1)/2` (b) `(sin3A)/(sinA)=(2k)/(k-1)` `(cot3A)/(cotA)=1/k` (d) none of these

A

`(cosA)/(cos3A)=(k-1)/(2)`

B

`(sin2A)/(sinA)=(2k)/(k-1)`

C

`(cos3A)/(cotA)=(1)/(k)`

D

none of these.

Text Solution

Verified by Experts

The correct Answer is:
D
`(tan 3A)/(tanA)=k(kne1)`
`therefore (sin3A cosA)/(cos A cos 3A)=(k)/(1)`
`therefore (k+1)/(k-1)=(sin4A)/(sin2A)=2cos2A` (using comp. and divd. )
`therefore (sin3A)/(sinA)=1+2cos2A=(2k)/(k-1)`
Similarly, `(cosA)/(cos3A)=(k-1)/(2)`
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