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Given that cos(x/2).cos(x/4).cos(x/8).....

Given that `cos(x/2).cos(x/4).cos(x/8)..... = sinx/x` Prove that `(1/2^2)sec^2(x/2) +(1/2^4)sec^2(x/4) +..... = cosec^2x - 1/(x^2)`

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AI Generated Solution

To prove the given equation, we start with the provided identity: \[ \cos\left(\frac{x}{2}\right) \cdot \cos\left(\frac{x}{4}\right) \cdot \cos\left(\frac{x}{8}\right) \cdots = \frac{\sin x}{x} \] ### Step 1: Taking the logarithm of both sides We take the logarithm of both sides to simplify the product on the left-hand side: ...
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