Question

If cosec31=x,then sin^2 59+1/cosec^2 31+tan^2 59-1/sin^2 59.cosec^2 59 is equal to​

Answer 1

$\frac{x^{2} - 1}{x^{2}} + 2x^{2} - 2$

Step-by-step explanation:

We are given that, $\csc 31^{\circ} = x$

⇒ $\sin 31^{\circ} = \frac{1}{x}$

⇒ $\sin (90^{\circ} - 59^{\circ}) = \frac{1}{x}$

⇒ $\cos 59^{\circ} = \frac{1}{x}$ ............ (1)

Now, $\sin^{2}59^{\circ} = 1 - \cos^{2}59^{\circ} = 1 - \frac{1}{x^{2}} = \frac{x^{2} - 1}{x^{2}}$ ............ (2)

Again, $\tan^{2} 59^{\circ} = \frac{\sin^{2}59^{\circ} }{\cos^{2}59^{\circ}} = x^{2} - 1$ {From equation (1) and (2)}

Finally, we have to evaluate,

$\sin^{2}59^{\circ} + \frac{1}{\csc^{2} 31^{\circ}} + \tan^{2}59^{\circ} - \frac{1}{\sin^{2}59^{\circ} \times \csc^{2}59^{\circ}}$

= $\frac{x^{2} - 1}{x^{2}} + x^{2} + x^{2} - 1 - \frac{\sin^{2} 59^{\circ} }{\sin^{2}59^{\circ} }$

= $\frac{x^{2} - 1}{x^{2}} + x^{2} + x^{2} - 1 - 1$

= $\frac{x^{2} - 1}{x^{2}} + 2x^{2} - 2$ (Answer)

Answer 2

Answer:

Step-by-step explanation: