Express theta - sqrt(3) theta in the form R (theta - lambda), and find the value of R and lambda.

April 13, 2026Mathematics

ScanSolve AI Answer

April 13, 2026

Answer

Hey Dany — ready when you are.

3. (ii) Step 1: Express $\sin \theta - \sqrt{3} \cos \theta$ in the form $R \sin(\theta - \lambda)$ . We compare $\sin \theta - \sqrt{3} \cos \theta$ with the expansion of $R \sin(\theta - \lambda)$ : $R \sin(\theta - \lambda) = R(\sin \theta \cos \lambda - \cos \theta \sin \lambda) = (R \cos \lambda) \sin \theta - (R \sin \lambda) \cos \theta$ Equating the coefficients of $\sin \theta$ and $\cos \theta$ :

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Asked on April 13, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 13, 2026

Hey Dany — ready when you are. 3. (ii) Step 1: Express - sqrt(3) in the form R ( - ). We compare - sqrt(3) with the expansion of R ( - ): R ( - ) = R( - ) = (R ) - (R ) Equating the coefficients of and : R = 1