Find the smallest positive value of x satisfying the equation logcos x sin x + logsin x cos x = 2
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Find the smallest positive value of x satisfying the equation logcos x sin x + logsin x cos x = 2
Find the smallest positive value of x satisfying the equation logcos x sin x + logsin x cos x = 2
Let logcos x sin x = p. Then, logsin x cos x = \(\frac{1}{p}\).
∴ log cos x sin x + log sin x cos x = 2
⇒ p + \(\frac{1}{p}\) = 2
⇒ p2 – 2p + 1 = 0
⇒ (p – 1)2 = 0
⇒ p = 1
⇒ log cos x sin x = 1
⇒ sin x = cos x
The smallest positive value of x for which sin x = cos x is x = \(\frac{\pi}{4}\) .