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Karthik M

The graph of the function :
y = cosxcos(x+2) - cos²(x+1) is

1. a straight line with slope 2
2. a straight line passing through origin
3. a parabola with vertex (1-sin²1, 1)
4. a straight line parallel to the x axis.

Please give a detailed explanation with graph, if possible.

Ramya Hegde

Its d., a line parallel to x-axis.

Now,

y=cosx. cos(x+2) -cos²(x+1)

(multiplying and dividing both terms by 2)

=1/2*[2cosx. cos(x+2)] -1/2*[2cos²(x+1)]

=1/2*[cos(2x+2) +cos2] -1/2*[1+cos(2x+2)]

(using, 2cosa.cosb=cos(a+b) +cos(a-b))

=1/2*[cos2-1]

= -(1-cos2)/2

= -(2sin²1)/2 (using, 1-cos2x=2sin²x)

= -sin²1

hence, its a line parallel to the x-axis.

Karthik M

Good solution. Thanks.

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