If `costheta=3/5 and pilttheta<(3pi)/2` find the values of other five trigonometric functions and hence evaluate`(cosectheta-cottheta)/(sectheta-tantheta)`.

Explanation

Given, `cos theta=frac(-3)(5)` and `pi `< `theta`<`frac(3 pi)(2)`,

`therefore
theta` lies in third quadrant. Therefore, in third quadrant

`sin theta` < `theta`, `cos theta`< `theta` and `tan theta>theta`.

We have, `sin ^(2) theta=1-cos ^(2) theta=frac(16)(25)`

`Rightarrow sin theta=pm frac(4)(5)` but `sin theta<0 .`

`therefore sin theta=-frac(4)(5)`;

`sec theta=frac(1)(cos theta)=frac(-5)(3)`,

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