Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2019  MayJun  (P19709/12)  Q#4
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Question
Angle x is such that sin x = a + b and cos x = a − b, where a and b are constants.
A curve is such that . The point P (2,9) lies on the curve.
i. Show that a2 +b2 has a constant value for all values of x.
ii. In the case where tan x = 2, express a in terms of b.
Solution
i.
We are given that;
Taking squares of both sides of both equations;


We have the algebraic formula;




Adding both equations;
We have the trigonometric identity;
Therefore;
Hence, has a constant value for all values of x.
ii.
We are given that;
Dividing both equations;
Since, ;
We are given that;
Hence;
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