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Prove the identity ((secy-tany) (secy+ tan y))/secy= COS U

User Alexzander
by
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1 Answer

4 votes

Answer:

boring

Explanation:

To prove the given identity, we'll start with the left side and simplify it step by step until we obtain the right side of the equation:

We have:

((sec y - tan y)(sec y + tan y)) / sec y

Using the difference of squares, we can rewrite the numerator:

((sec y)^2 - (tan y)^2) / sec y

Recall the trigonometric identity: (sec x)^2 - (tan x)^2 = 1

Substituting this identity into our expression:

(1) / sec y

Using the reciprocal identity: sec x = 1 / cos x

We can rewrite the expression as:

1 / (1 / cos y)

Simplifying further by multiplying by the reciprocal:

cos y / 1

Which simplifies to:

cos y

Therefore, we have shown that the left side of the identity ((sec y - tan y)(sec y + tan y)) / sec y simplifies to cos y, which is the same as the right side of the equation.

User Migu
by
8.3k points

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