A Level Trigonometry identities (sec, cosec, cot)

[bright ibex]

Can someone, step by step show how the LHS is identical to the RHS?

Thanks!

[hollow cosmos]

did you replace cot and tan in terms of sin and cos

After you combine denominators, the denominator reduces to 1 using ||the Pythagorean identity||

[bright ibex]

Yes

So, cos/sin + sin/cos

But I legit don't know where to go after that... Like, how I go from a sum to a product.

[hollow cosmos]

common denominators, in this case that is ||cos sin||

[bright ibex]

?

I mean the denominators are sin and cos.

They aren't common

[hollow cosmos]

I meant rewrite the fractions to have common denominators.

Like how you would do $\frac{1}{3}+\frac{4}{7}$

[marble harness]

Civil Service Exam is good

[bright ibex]

Right

so

1 + sin cos

(sin/cos) + (cos/sin)
= (cos sin) + (sin cos) / sincos
= 1 + cos sin

[hollow cosmos]

it should be $\frac{\cos^2 +\sin^2}{\sin \cos}$ tbh

[marble harness]

Civil Service Exam is good

[bright ibex]

right