Standard +0.8 This requires implicit differentiation of a trigonometric relation, then algebraic manipulation using multiple trig identities (sec²x = 1 + tan²x, cos²y = 1 - sin²y, double angle formula cos 2x = cos²x - sin²x) to reach the target form. The multi-step manipulation to eliminate y and simplify to the given expression elevates this beyond routine implicit differentiation.
State \(\cos y\frac{dy}{dx}\) as derivative of \(\sin y\)
B1
State correct derivative in terms of \(x\) and \(y\), e.g. \(\sec^2 x/\cos y\)
B1
State correct derivative in terms of \(x\), e.g. \(\frac{\sec^2 x}{\sqrt{1-\tan^2 x}}\)
B1
Use double angle formula
M1
Obtain the given answer correctly
A1
## Question 5:
| Answer | Mark | Guidance |
|--------|------|----------|
| State $\cos y\frac{dy}{dx}$ as derivative of $\sin y$ | B1 | |
| State correct derivative in terms of $x$ and $y$, e.g. $\sec^2 x/\cos y$ | B1 | |
| State correct derivative in terms of $x$, e.g. $\frac{\sec^2 x}{\sqrt{1-\tan^2 x}}$ | B1 | |
| Use double angle formula | M1 | |
| Obtain the given answer correctly | A1 | |