Equation in powers of sixteen with squared sine and cosine exponents, solved by substitution

IB Year 6 | Grade 12

6 marks

Solve the equation \(16^{\sin^2x}+16^{\cos^2x}=10\) for \(0\le x\le\pi\).[6]

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Answer:\(x=\frac{\pi}{6},\ \frac{\pi}{3},\ \frac{2\pi}{3},\ \frac{5\pi}{6}\)

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