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## Homework Statement

Prove that

[tan(a) + 1][cot(a+pi/4) + 1] = 2

## Homework Equations

[tan(a) + 1][cot(a+pi/4) + 1] = 2

## The Attempt at a Solution

This was very hard, I tried my best at expanding.

[tan(a) + 1][cot(a+pi/4) + 1] = tan(a)cot(a+pi/4) + tan(a) + cot(a+pi/4) + 1

The issue is that there is no cofuntion identity for cot(a + pi/4) so I did

cot(a + pi/4) = cot([a - pi/4] + pi/2]) Let b = a - pi/4 thus,

cot(b + pi/2) = -tan(b) = -tan(a - pi/4)

This doesnt help AT ALL.

Any help?

Thanks