Standard +0.3 This question requires finding cos θ from sec θ, then sin θ using Pythagorean identity, then tan θ, and finally applying the compound angle formula for tan(θ + π/4). While it involves multiple steps and reciprocal trig functions, each step follows standard procedures with no novel insight required. The compound angle formula with π/4 is particularly routine since tan(π/4) = 1 simplifies the calculation. This is slightly easier than average due to the straightforward chain of standard techniques.
Use identity \(\sec^2\theta = 1 + \tan^2\theta\) to find value of \(\tan\theta\)
M1
OE using \(\cos\theta = \frac{1}{\sqrt{17}}\) and \(\sin\theta = \frac{4}{\sqrt{17}}\) values
Obtain \(\tan\theta = 4\)
A1
Condone inclusion of \(\tan\theta = -4\)
State or imply \(\tan(\theta + \frac{1}{4}\pi) = \frac{\tan\theta + \tan\frac{1}{4}\pi}{1 - \tan\theta\tan\frac{1}{4}\pi}\) and substitute value of \(\tan\theta\)
M1
OE
Obtain \(-\frac{5}{3}\) or exact equivalent only
A1
## Question 3:
| Answer | Mark | Guidance |
|--------|------|----------|
| Use identity $\sec^2\theta = 1 + \tan^2\theta$ to find value of $\tan\theta$ | M1 | OE using $\cos\theta = \frac{1}{\sqrt{17}}$ and $\sin\theta = \frac{4}{\sqrt{17}}$ values |
| Obtain $\tan\theta = 4$ | A1 | Condone inclusion of $\tan\theta = -4$ |
| State or imply $\tan(\theta + \frac{1}{4}\pi) = \frac{\tan\theta + \tan\frac{1}{4}\pi}{1 - \tan\theta\tan\frac{1}{4}\pi}$ and substitute value of $\tan\theta$ | M1 | OE |
| Obtain $-\frac{5}{3}$ or exact equivalent only | A1 | |
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