Solve the equation sin x – 1 = cos x graphically on the interval [0,2pi]. Sketch the graph, and list the solutions.
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The equation sin x - 1 = cos x has to be solved.
sin x - 1 = cos x
=> sin x - cos x = 1
The graph of y = sin x - cos x is:
Take the square of both the sides
=> `sin^2 x + cos^2x - 2*cos x*sin x = 1`
=> `1 - 2*cos x*sin x = 1`
=> `-2*cos x*sin x = 0`
=> `sin 2x = 0`
=> `2x = 0` and `2x = pi` and `2x = 2*pi`
=> x = 0 and x = `pi/2` and x = `pi`
But as sin 0 - cos 0 = -1 eliminate x = 0.
The solution of the equation is x = `pi/2` degrees and x = `pi`
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