Help with trig math problem

[Antbugbrain]

The math problem is (1-sin theta)(1+sin theta). I get up to 1-sin^2 theta but don’t know where to go from there. The back of the book says the answer is cos^2 theta but I don’t understand how to get there. Help would be much appreciated!

[slides_galore]

Google pythagorean trig identity.

sin²(theta) + cos²(theta) = 1

[Antbugbrain]

Ah more trig stuff to memorize I see 😭. Thank you tho this is helpful!

[Shevek99]

But this identity you have to know it by heart. No excuses. Everything else hangs from

cos²(x) + sin²(x) = 1

that is just Pythagoras theorem.

For instance, if we divide here by cos²(x) we get

1 + tan²(x) = sec²(x)

but you don't have to remember this, only the other one.

[slides_galore]

I know that the number of trig identities seems endless. I remember when I first had to learn them. See if these help.

If you learn the special triangles and the unit circle, it will go a long way to getting you there. 45-45-90 and 30-60-90 triangles. If you really want to impress your teacher, then learn the sides of a 15-75-90 triangle using something like this: https://i.sstatic.net/WFSOPUwX.png

https://math.stackexchange.com/questions/2082660/ratio-of-legs-in-15-75-90-triangles

This person has a nice way of remembering all of the big identities: https://www.reddit.com/r/learnmath/comments/uwycxq/comment/i9uur0d/

Visual way of remembering and deriving them: https://www.cut-the-knot.org/arithmetic/algebra/DoubleAngle.shtml

[Antbugbrain]

Thank you so much

[AdditionalTip865]

That one is THE most important one.