If sin ⁡ x sin ⁡ y = 3 and cos ⁡ x cos ⁡...

landdenaw

landdenaw

Answered

2022-06-24

If sin x sin y = 3 and cos x cos y = 1 2 , then find sin 2 x sin 2 y + cos 2 x cos 2 y

Answer & Explanation

Eli Shaffer

Eli Shaffer

Expert

2022-06-25Added 16 answers

sin y = 3 sin x and cos y = 2 cos x
Thus,
1 = sin 2 y + cos 2 y = 9 sin 2 x + 4 cos 2 x = 4 + 5 sin 2 x ,
which is impossible.If sin y = 1 3 sin x we obtain:
1 = sin 2 y + cos 2 y = 1 9 sin 2 x + 4 cos 2 x = 1 9 + 35 9 sin 2 x .
Now, you can get sin 2 x, sin 2 y and the rest for you.
aligass2004yi

aligass2004yi

Expert

2022-06-26Added 7 answers

hint
sin ( y ) = 1 3 sin ( x )
cos ( y ) = 2 cos ( x )
sin 2 ( x ) + 36 cos 2 ( x ) = 9
35 cos 2 ( x ) = 8
cos 2 ( x ) = 8 35
the second expression is
16 35 64 35 = 19 / 29
the final result is
3 / 2 19 / 29 = 49 / 58

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