Standard +0.8 This question requires expanding tan(θ-60°) using the compound angle formula, converting cot θ to 1/tan θ, then solving a resulting quadratic in tan θ. It demands multiple techniques (compound angles, trigonometric identities, algebraic manipulation) and careful handling of the restricted domain, making it moderately harder than a standard single-technique trigonometric equation.
Condone sign errors in first step and retention of tan60.
Obtain tan2−4 3tan−3=0
A1
OE involving decimals.
Solve 3-term quadratic equation to obtain at least one value of
M1
Obtain −22.2 and 82.2
A1
Or greater accuracy; and no others between –90 and 90.
5
Answer
Marks
Guidance
Question
Answer
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Question 2:
2 | tan−tan60 3
State =
1+tantan60 tan | B1 | OE involving tan only.
Attempt arrangement of equation to quadratic form | M1 | Condone sign errors in first step and retention of tan60.
Obtain tan2−4 3tan−3=0 | A1 | OE involving decimals.
Solve 3-term quadratic equation to obtain at least one value of | M1
Obtain −22.2 and 82.2 | A1 | Or greater accuracy; and no others between –90 and 90.
5
Question | Answer | Marks | Guidance