A-LevelMathematicsTrigonometry9709/33 · Oct/Nov 2022 · Q78 Marks
Show that the equation √5 secx + tanx = 4 can be expressed as Rcos(x + α) = √5, where R > 0 and 0° < α < 90°. Give the exact value of R and the value of α correct to 2 decimal places.
- (a)Show that the equation √5 secx + tanx = 4 can be expressed as Rcos(x + α) = √5, where R > 0 and 0° < α < 90°. Give the exact value of R and the value of α correct to 2 decimal places.[4]
- (b)Hence solve the equation √5 sec 2x + tan 2x = 4, for 0° < x < 180°.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.
- B1 Rearrange and obtain 4 cosx-sinx = √5
- B1 State R = √17
- M1 Use trig formulae to find α
- A1 Obtain α = 14.04°
- B1 FT Evaluate cos⁻¹(√5/√17) FT their R.
- M1 Carry out a correct method to find a value of x in the given interval
- A1 Obtain answer, e.g. 21.6°
- A1 Obtain a second answer, e.g. 144.4° and no other in the interval
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