Find the value of (sin$$^6$$​A + cos$$^6$$​A + 3sin$$^2$$​A cos$$^2$$​A) - (sin$$^4$$​A - cos$$^4$$​A + 1) cosec$$^2$$​A.

Correct option is D

Given:​

(sin$$^6$$​​A + cos$$^6$$​​A + 3sin$$^2$$​​A cos$$^2$$​​A) - (sin$$^4$$​​A - cos$$^4$$​​A + 1) cosec$$^2$$​​A.

Solution:

Put A = 45$$^\circ$$

​(sin$$^6$$​​​A + cos$$^6$$​​​A + 3sin$$^2$$​​​A cos$$^2$$​​​A) - (sin$$^4$$​​​A - cos$$^4$$​​​A + 1) cosec$$^2$$​​​A.

=$$\left (\frac18+\frac 18+\frac 34\right)-\left (\frac14-\frac 14 +1\right) 2$$​​

= $$\left (\frac{1+1+6}{8}\right)-2$$

=$$\frac 88-2= 1-2=-1$$​​