A-LevelMathematicsTrigonometry9709/31 · Oct/Nov 2018 · Q68 Marks
Show that the equation (√2) cosec x + cot x = √3 can be expressed in the form R sin(x − α) = √2, where R > 0 and 0° < α < 90°.
- (i)Show that the equation (√2) cosec x + cot x = √3 can be expressed in the form R sin(x − α) = √2, where R > 0 and 0° < α < 90°.[4]
- (ii)Hence solve the equation (√2) cosec x + cot x = √3, for 0° < x < 180°.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [B1] (i) Rearrange in the form √3sinx - cosx = √2
- [B1] (i) State R = 2
- [M1] (i) Use trig formulae to obtain α
- [A1] (i) Obtain α = 30° with no errors seen
- [B1ft] (ii) Evaluate sin⁻¹(√2/R)
- [M1] (ii) Carry out a correct method to find a value of x in the given interval
- [A1] (ii) Obtain answer x = 75°
- [A1ft] (ii) Obtain a second answer e.g. x = 165° and no others
- [Treat answers in radians as a misread. Ignore answers outside the given interval.]
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →