Question

answer this plz
if a cosX - b sinX=c, Prove that a sinX + b cosX= √a^2+b^2+c^2

Answer 1

on squaring both sides
a²cos²x + b²sin²x - 2ab sinx cosx = c²
a²(1-sin²x) + b²(1-cos²x) -2ab sinx cosx = c²
a²- a²sin²x + b² - b²cos²x -2ab sinx cosx = c²
a²-b²-c²= a²sin²x + b²cos²x +2ab sinx cosx
a²+b²-c²= (asinx + bcosx)²
asinx + bcosx = √a²+b²-c²
HENCE PROVED.

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