Question
Finding Constants Determine the constants $a$ and $b$ such that $$\sin x+\cos x=a \sin (x+b)$$Use this result to integrate $$\int \frac{d x}{\sin x+\cos x}$$
Step 1
Step 1: Express \( a \sin(x + b) \) using the angle addition formula for sine: \[ a \sin(x + b) = a (\sin x \cos b + \cos x \sin b) \] This can be rewritten as: \[ a \sin(x + b) = a \cos b \sin x + a \sin b \cos x \] Show more…
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