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If int0^(pi//2) log sin x dx=k, then the...

If `int_0^(pi//2) log sin x dx=k`, then the value of the definite integral `int_0^(pi//4) log (1+tan theta) d theta` (i) `-K/8` (ii)`-K/4` (iii) `K/8` (iv )`K/4`

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