Help in understanding something in trigonometry

Question

If sin∝ = cos β

,then ∝ ± β = 90° + 360°n

If tan ∝ = cot β

,then ∝ + β = 90° + 180°n

I can't really get this. I hope someone could explain it to me. Thanks for any help in advance

Answer 1

I haven't got this either, but I can give you a start now and if I think of something later, I will let you know.

The only times the sin and cos can possibly be equal is when the angles are in the 1st or 3rd quadrant; otherwise, they have opposite signs.

Now draw a figure of an angle the first quadrant. If sin of this angle is the same as the cos of another angle, where is the 2nd angle? Right, it is the complementary angle, i.e. the 2 angles are complements as stated. I can't say anything about the difference of the 2 angles.

Now the tan and cot always have the same sign; therefore, they can be equal in all 4 quadrants and the pictures again show that the angles are complementary. Again I can't say anything about the difference of the 2 angles.

I hope that helps a little!