9. (a) Prove that
sin 2x - tan x = tan x cos 2x,
x ≠ (2n + 1)90°, n ∈ Z
(b) Given that x ≠ 90° and x ≠ 270°, solve, for 0 ≤ x < 360°,
sin 2x - tan x = 3 tan x sin x
Give your answers in degrees to one decimal place where appropriate - Edexcel - A-Level Maths Pure - Question 1 - 2016 - Paper 4
Question 1
9. (a) Prove that
sin 2x - tan x = tan x cos 2x,
x ≠ (2n + 1)90°, n ∈ Z
(b) Given that x ≠ 90° and x ≠ 270°, solve, for 0 ≤ x < 360°,
sin 2x - tan x = 3 ta... show full transcript
Worked Solution & Example Answer:9. (a) Prove that
sin 2x - tan x = tan x cos 2x,
x ≠ (2n + 1)90°, n ∈ Z
(b) Given that x ≠ 90° and x ≠ 270°, solve, for 0 ≤ x < 360°,
sin 2x - tan x = 3 tan x sin x
Give your answers in degrees to one decimal place where appropriate - Edexcel - A-Level Maths Pure - Question 1 - 2016 - Paper 4
Step 1
Prove that sin 2x - tan x = tan x cos 2x
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Answer
To prove the equation, we start with the left-hand side:
sin 2x = 2 sin x cos x \\
2 sin x cos x = 4 \frac{sin^2 x}{cos x} \\
\Rightarrow 2sin x cos^2 x = 4 sin^2 x \\
\Rightarrow 2cos^2 x = 4sin x \\
\Rightarrow cos^2 x = 2sin x \\
\Rightarrow cos^2 x - 2sin x = 0$$
Factoring results in:
(cos^2 x)(1) - (2)(sin x) = 0
Using identities for solutions:
Thus, solutions yield:
- $16.3°$
- $163.7°$
- $180°$
