The numerical value of $$1+\frac{1}{\cot^{2}63^{\circ}}-\sec^{2}27^{\circ}+\frac{1}{\sin^{2}63^{\circ}}-cosec^{2}27^{\circ}$$ is

We need to find the value of $$1+\frac{1}{\cot^{2}63^{\circ}}-\sec^{2}27^{\circ}+\frac{1}{\sin^{2}63^{\circ}}-cosec^{2}27^{\circ}$$

we know that ,

$$\frac{1}{cot^2 \theta}$$ = $$tan^2 \theta$$.............(1)

$$\frac{1}{sin^2 \theta}$$ = $$cosec^2 \theta$$...........(2)

and 1 + $$tan^2 \theta$$ = $$sec^2 \theta$$.................(3)

Using equations 1 ,2 and 3

= $$1+\frac{1}{\cot^{2}63^{\circ}}-\sec^{2}27^{\circ}+\frac{1}{\sin^{2}63^{\circ}}-cosec^{2}27^{\circ}$$

= 1 + $$tan^2 63$$ - $$sec^2 27$$ + $$cosec^2 63$$ - $$cosec^2 27$$

= $$sec^2 63$$ - $$sec^2 27$$ + $$cosec^2 63$$ - $$cosec^2 27$$

= $$sec^2 (90-27)$$ - $$sec^2 27$$ + $$cosec^2 (90-27)$$ - $$cosec^2 27$$

=$$cosec^2 27$$ - $$sec^2 27$$ + $$sec^2 27$$ - $$cosec^2 27$$

= 0