What is the Derivative of the Infinite Series of Tangent Powers?

[cj5892]

Homework Statement

Consider the infinite series s(x)=1-tan^2(x)+tan^4(x)-tan^6(x)+... , where 0<x<pi/4
s'(x)=
A.sin2x
B.cos2x
C.-tan2x
D.-sin2x
E.-cos2x

The Attempt at a Solution

Attempting to derive the series, i get 1-2tanxsec^2x+4tan^3(x)sec^2(x)-6tan^5(x)sec^2(x)+...

am i missing something obvious here? i don't see any trig identities in that that would give any of the answers

 

[LCKurtz]

Homework Statement

Consider the infinite series s(x)=1-tan^2(x)+tan^4(x)-tan^6(x)+... , where 0<x<pi/4
s'(x)=
A.sin2x
B.cos2x
C.-tan2x
D.-sin2x
E.-cos2x

The Attempt at a Solution

Attempting to derive the series, i get 1-2tanxsec^2x+4tan^3(x)sec^2(x)-6tan^5(x)sec^2(x)+...

am i missing something obvious here? i don't see any trig identities in that that would give any of the answers

Hint: Sum that geometric series for s(x) first.

 

[cj5892]

i still can't get it :(

 

[Dick]

i still can't get it :(

What's the series expansion of 1/(1+r)?

 

[LCKurtz]

Or what is the sum of a geometric series with first term a and ratio r?