Question

1-cos2a/2cosa=sina.tana​

Answer 1

see explanation

Explanation:

using the trigonometric identities

• cos2a = 1 - 2sin²a

• tana =
`(sina)/(cosa)`

consider the left side

`(1-cos2a)/(2cosa)`

=
`(1-(1-2sin^2a))/(2cosa)`

=
`(1-1+2sin^2a)/(2cosa)`

=
`(2sin^2a)/(2cos^2a)` ← cancel the 2 on the numerator/ denominator

=
`(sin^2a)/(cosa)`

= sina ×
`(sina)/(cosa)`

= sina × tana

= sinatana

= right side