Find the value of cos 225

We have to find the value of cos 225

Solution

cos 225 can be expressed as

cos 225= cos (180 +45)

We know the identity

cos(A+B)=cos(A)⋅cos(B)−sin(A)⋅sin(B)

Hence

cos (180 + 45) = cos 180. cos 45 – sin 180.sin 45

Substituting the values of the above angles we get

cos 180= -1

cos 45=√2/2

sin 180 =0

sin 45= √2/2

cos (180 + 45) = -1 .(√2/2) – 0 . (√2/2)

= -√2/2

= – √2/2

cos 225 = – √2/2

Answer

cos 225 = – √2/2

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