Trigonometric identities

[lean terrace]

<@&286206848099549185>

[twilit nest]

1/(sin^2(x) cos^2(x)) = (1/sin^2(x)) * (1/cos^2(x)) = (1/sin(x))^2 * (1/cos(x))^2 and then substitute.

[lean terrace]

Sorry can you visualize it for me actual fraction, I get confused with / like that

@twilit nest

[shell kestrel]

$\frac{1}{\sin^2{x}\cos^2{x}} = \frac{1}{\sin^2{x}\times\cos^2{x}}$

$= \frac{1}{\sin^2{x}}\times\frac{1}{\cos^2{x}}$

$= \left(\frac{1}{\sin{x}}\right)^2\times\left(\frac{1}{\cos{x}}\right)^2$

$= \left(\csc{x}\right)^2\times\left(\sec{x}\right)^2$

$= \csc^2{x}\sec^2{x}$

[karmic juniper]

Jay

[twilit nest]

like this?

[lean terrace]

wait

why is there a square on sec^2

[shell kestrel]

It's a write-o... like a type-o, but when you write it. 🙂

[lean terrace]

So basically, trig indentities is just manipulations?

Cuz I struggle manipulate some equation

[shell kestrel]

A lot of it is manipulations, but there are good reasons for wanting some of those manipulations.

For example, an identity A = B might make solving the equation A = 1 easier because B = 1 is more approachable.

Or, in some problems, two students who get different answers A and B should both be credited if A = B is an identity.

Yes, plenty of questions are just playing the game about manipulations but that doesn't make the skill behind them unimportant or unhelpful.