A-LevelMathematicsTrigonometry9709/33 · May/June 2018 · Q58 Marks
5
- (i)By first expanding (cos²x + sin²x)³, or otherwise, show that cos⁶x + sin⁶x = 1 - (3/4)sin²2x.[4]
- (ii)Hence solve the equation cos⁶x + sin⁶x = 3/5, for 0° < x < 180°.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- M1 Attempt cubic expansion and equate to 1
- A1 Obtain a correct equation
- M1 Use Pythagoras and double angle formula in the expansion
- A1 Obtain the given result correctly
- M1 Use the identity and carry out a method for finding a root
- A1 Obtain answer 20.9°
- A1FT Obtain a second answer, e.g. 69.1°
- A1FT Obtain the remaining answers, e.g. 110.9° and 159.1°, and no others in 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 →