The expression cot(theta) x sec(theta) is equivalent to
a) cos(theta) / sin^2(theta)
I am pretty sure these are trig proofs. But I can't figure them out, a quick thoroughly described answer would be great.
Mathematically your statements are incorrect. Let's invetigate one at a time.
In general csc of an angle is not equal to the sec of that angle. They are equal if `theta=45+nPi`
`costheta/sintheta*1/costheta=1/sintheta` when `costheta!=0, theta!=Pi/2+nPi`
Here also in general `1/sintheta!=sintheta`
We are given the expression `cot theta*sec theta` :
Expressing these in terms of sin and cos yields:
This product is `1/sintheta=csctheta`
So neither (a) nor (b) are correct simplifications or identities since
(a) `costheta/(sin^2theta)=cottheta*1/sintheta=cottheta*csctheta` and
are neither equivalent to `cotthetasectheta` .