10sqrt(2)[sin(X +45deg)] +14cosX = A*sinX +B*cosX

10sqrt(2)[sinXcos(45deg) +cosXsin(45deg)] +14cosX = A*sinX +B*cosX

10sqrt(2)[sinX(1 /sqrt(2)) +cosX(1 /sqrt(2))] +14cosX = A*sinX +B*cosX

10[sinX +cosX] +14cosX = A*sinX +B*cosX

10sinX +24cosX = A*sinX +B*cosX

Therefore, A = 10, asnd B = 24 -------------answer.

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The last part, where it is suggested to express

10sqrt(2)[sin(X +45deg)] +14cosX

into

R*sin(X +a),

I don't quite understand it.