prove that siny*cosy*tany=1-cos^2y

Asked on by fortunee

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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We'll manage the left side writting `tan y = sin y/cos y` .

We'll re-write the given expression:

`sin y*cos y*(siny/cosy) = 1 - cos^2 y`

We'll simplify by cos y to the left side:

`sin y*sin y = 1 - cos ^2 y`

`sin^2 y = 1 - cos ^2 y`

We'll add `cos^2 y ` both sides:

`sin^2 y + cos^2 y = 1`

Since we've get the Pythagorean identity, the given expression represents an identity.

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