Standard +0.3 This is a straightforward multiple angle trigonometric equation requiring the identity sec²x = 1 + tan²x to convert to a quadratic in tan 2θ, then solving and finding angles in the given range. While it involves reciprocal trig functions and double angles, the method is standard and mechanical with no novel insight required, making it slightly easier than average.
Use trig identity correctly to obtain a quadratic in \(\tan 2\theta\)
M1
Solve the quadratic correctly
M1
Obtain \(\tan 2\theta = 1\) or \(-\frac{4}{5}\)
A1
Obtain one correct answer
A1
Carry out correct method for second answer from either root
M1
Obtain remaining 3 answers from \(22.5°, 112.5°, 70.7°, 160.7°\) and no others in the range [Ignore answers outside the given range]
A1
[6]
Use trig identity correctly to obtain a quadratic in $\tan 2\theta$ | M1 |
Solve the quadratic correctly | M1 |
Obtain $\tan 2\theta = 1$ or $-\frac{4}{5}$ | A1 |
Obtain one correct answer | A1 |
Carry out correct method for second answer from either root | M1 |
Obtain remaining 3 answers from $22.5°, 112.5°, 70.7°, 160.7°$ and no others in the range [Ignore answers outside the given range] | A1 | [6]