Moderate -0.8 This is a straightforward application of fundamental trigonometric identities (Pythagorean identity and tan definition). For an acute angle, it requires recognizing that √(1-cos²θ) = sinθ, then simplifying sinθ/tanθ = sinθ/(sinθ/cosθ) = cosθ. This is simpler than average A-level questions as it's pure algebraic manipulation with basic identities and no problem-solving or multi-step reasoning required.
\(\frac{\sqrt{\sin^2\theta}}{\sin\theta}\) or \(\frac{\cos\theta\sqrt{\sin^2\theta}}{\sin\theta}\) divided by \(\frac{\sin\theta}{\cos\theta}\)
M1
correct substitution for numerator; allow maximum of M1M1 if \(\pm\sqrt{\sin^2\theta}\) oe substituted
M1
correct substitution for denominator
\(\cos\theta\) cao
A1
A0 if follows wrong working or B3 www or if unsupported; mark the final answer but ignore attempts to solve for \(\theta\); allow recovery from omission of \(\theta\)
## Question 3:
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\frac{\sqrt{\sin^2\theta}}{\sin\theta}$ or $\frac{\cos\theta\sqrt{\sin^2\theta}}{\sin\theta}$ divided by $\frac{\sin\theta}{\cos\theta}$ | M1 | correct substitution for numerator; allow maximum of M1M1 if $\pm\sqrt{\sin^2\theta}$ oe substituted |
| | M1 | correct substitution for denominator |
| $\cos\theta$ cao | A1 | A0 if follows wrong working or B3 www or if unsupported; mark the final answer but ignore attempts to solve for $\theta$; allow recovery from omission of $\theta$ |
---