Prove that `("cos"(90^0+theta)"sec"(-theta)"tan"(180^0-theta))/("sec"(360^0-theta)"sin"(180^0+theta)"cot"(90^0-theta))=-1.`

Explanation

`cos (90^{circ}+theta)=-sin theta`

`sec (-theta)=sec theta`

`tan (180^{circ}-theta)=-tan theta`

`sec (360^{circ}-theta)=sec theta`

`sin (180^{circ}+theta)=-sin theta`

`cot (90^{circ}-theta)=tan theta`

`therefore frac{cos (90^{circ}+theta) sec (-theta) tan (180^{circ}-theta)}{sec (360^{circ}-theta) sin (180^{circ}+theta) cot (90^{circ}-theta)}`

`=frac{(-sin theta)(sec theta)(-tan theta)}{(sec theta)(-sin theta)(tan theta)}=-1`