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(1-cos 40^(@))/(2)=...

`(1-cos 40^(@))/(2)=`

A

`cos^(2)20^(@)`

B

`sin^(2)20^(@)`

C

`tan 20^(@)`

D

`cos 20^(@)`

Text Solution

Verified by Experts

The correct Answer is:
B
You will need an identity equation into which the expression `(1-cos 40^(@))/(2)` can fir. One of the half - angle identities is
`sqrt((1-cos A)/(2)=sin.(1)/(2)a`
It follows that `(sqrt((1-cos A)/(2)))^(2)=(sin.(1)/(2)a)^(2)`. Therefore, `(1-cos A)/(2)="sin"^(2)(1)/(2)a`
So `(1-cos 40^(@))/(2)="sin"^(2)(1)/(2)(40^(@))=sin 20^(@)`.
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