Given that 5cos⁡(x)−12sin⁡(x)=13 Im

Adrian Cervantes

Adrian Cervantes

Answered

2022-01-27

Given that
5cos(x)12sin(x)=13
Im

Answer & Explanation

becky4208fj

becky4208fj

Expert

2022-01-28Added 10 answers

Hint By Cauchy Schwarz you have
169=132=(5cos(x)12sin(x))2(52+122)(cos2(x)+sin2(x))=169
Therefore, you must have equality in CS, and hence
cos(x)5=sin(x)12
Now combine this equality with
sin2(x)+cos2(x)=1

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