If $$\tan \theta$$​ = 1 ($$\theta$$  is an acute angle) then the value of $$2 \sin \theta \cos \theta - \cosec^2 \theta$$​  is: 

Correct option is A

Given:

$$\tan \theta = 1$$​, and θ is an acute angle.

Formula Used:

​$$\tan 45\degree = 1 ,\quad \sin45\degree = \frac1{\sqrt2},\quad \cos45\degree = \frac1{\sqrt2}$$

$$\cosec 45\degree = \sqrt2$$​​

Solution:

From,

​$$\tan \theta = 1$$​​

$$\theta = 45^\circ$$​ (since it is an acute angle)

Now, 

​$$2\sin\theta \cos\theta - \cosec^2 \theta\\ \ \\ = 2\sin45\degree \cos45\degree - \cosec^2 45\degree\\ \ \\ = 2 \times \frac1{\sqrt2}\times \frac1{\sqrt2}- (\sqrt{2})^2 \\ \ \\ = 1-2 = -1$$​​