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saul85 [17]
3 years ago
11

Verify the identity cos quantity x plus pi divided by two = -sin x

Mathematics
1 answer:
In-s [12.5K]3 years ago
6 0

Answer:

Identity is verified.

Step-by-step explanation:

We have to verify the identity cos(x+\frac{\pi }{2}) = (- sinx)

To prove any identity we always prove one side(either left hand side or right hand side) of the equation equal to the other side.

In this identity we take the left hand side first

cos(x+\frac{\pi}{2})

=cosx\times cos(\pi/2)-sinx\times sin(\pi/2))  (as we know cos(a+b) = cosa×cosb-sina×sinb)

= cosx\times0-sinx\times1

= 0-sinx

= - sinx ( Right hand side)

Hence identity is proved.

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