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.