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Alternative Direct Substitution Approach Start from the given equation: [ costheta + sintheta = sqrt{2}costheta. ] Rearranging, we get: [ sintheta = (sqrt{2}-1)costheta. ] Now consider what we need to prove: [ costheta – sintheta = sqrt{2}sintheta. ] Substitute (sintheta = (sqrt{2}-1)costheta) into the left-hand side: [ costheta – sintheta = costheta – (sqrt{2}-1)costheta = …

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