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I am usin x in cas of theta-------------->

so 5 cosx=13-12 sinx

squaring on both sides we get,

25 cos²x=169+144 sin²x-312 sinx

in case of cos²x we substitute (1-sin²x),as sin²x+cos²x=1
equation will be 169 sin²x-312 sinx+144=0
after using quadratic formula we get sinx=312/338
so sinx =12/13.
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