Question

Can someone help me simplify these trig expressions?

Answer 1

\[\frac{ \tanθ\csc^2θ}{ 1+\tan^2θ }\]

I'm not sure what to do after diving the numerator and denominator by by tanθ

Answer 2

\[1+\tan^2(\theta)=\sec^2(\theta)\]

Answer 3

Substitute this expression into the problem

Answer 4

um so do csc^2θ/sec^2θ cancel out or something? im sorry this is my first time doing this :/

Answer 5

sec(x)=1/cos (x)
csc(x)=1/sin(x)
tan (x)= sin/cos
tan (x) (cos(x))^2/(sin(x))^2

Answer 6

=cos x/sin x= cot (x)

Answer 7

solving trig is just trial and error. If you don't try you will never get anywhere

Answer 8

Haha yeah I wasn't actually really looking for a direct answer, but thanks for that, I just needed to understand this better but it makes a bit more sense now I guess

Answer 9

it helps to be looking at all the trig identies when trying to solve

Answer 10

If no fancy identities strike immediately, worst case you can simplify the given expression by converting everything to sin and cos

Answer 11

Sorry but I'm still a bit confused as to how (tanx*csc^2x)/secx=(cos(x))^2/(sin(x))^2?

Answer 12

left hand side is ` (tanx*csc^2x)/sec^2x`

yes ?

Answer 13

we have

```
csc^2 = 1/sin^2

sec^2 = 1/cos^2
```


so
```
csc^2/sec^2 = cos^2/sin^2 = cot^2
```

Answer 14

Ah I see, thanks!!!