Solving simultaneous trigonometric equations Question: Solve the following equations for x and y sin(y)=sin(x−y) cos(x)=sin(x−y) where x,y in [0,pi/2]

akuzativo617

akuzativo617

Answered question

2022-11-15

Solving simultaneous trigonometric equations
Question: Solve the following equations for x and y
sin ( y ) = sin ( x y )
cos ( x ) = sin ( x y )
where x , y [ 0 , π 2 ]
My attempt:
The beginning of the solution seems to have something to do with
( i ) y = π 2 + x ( i i ) y = π 2 x
However I cannot understand how this conclusion was made.

Answer & Explanation

Zoe Andersen

Zoe Andersen

Beginner2022-11-16Added 16 answers

Hint: Use trigonometric complementary angle formula
sin ( y ) = cos ( x ) = sin ( π / 2 x )

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