1.

If a cos theta- b sin theta =c, then a sin theta+ b cos theta =

Answer»

answer:±√(a²+b²-c²)

Given, a cos θ - b sin θ = c 

Squaring both sides, 

a² cos² θ + b² sin² θ - 2ab sin θ cos θ = c² 

∴ a² ( 1 - sin² θ ) + b² ( 1 - cos² θ ) - 2ab sin θ cos θ = c² 

∴ a² - a² sin² θ + b² - b² cos² θ - 2ab sin θ cos θ = c² 

∴ a² + b² - c² = a² sin² θ + b² cos² θ + 2ab sin θ cos θ 

∴ ( √(a²+b²-c²) )² = ( a sin θ + b cos θ )² 

∴ a sin θ + b cos θ = ± √(a²+b²-c²)



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