Find the value of 3(sec$$^2$$​A-1)(cosecA - 1)(cosecA + 1) + 4(cosec$$^2$$​A - cot$$^2$$​A).

Correct option is C

Given:​

3(sec$$^2$$​​A-1)(cosecA - 1)(cosecA + 1) + 4(cosec$$^2$$​​A - cot$$^2$$​​A)

Formula Used:​

cosec²A - cot²A = 1

sec²A - tan²A = 1

tan A cot A = 1

Solution:​

​3(sec$$^2$$​​​A-1)(cosecA - 1)(cosecA + 1) + 4(cosec$$^2$$​​​A - cot$$^2$$​​​A)

=3(sec$$^2$$​​​A-1)(cosec²​A - 1) + 4(cosec$$^2$$​​​A - cot$$^2$$​​​A)

= 3tan²A cot²A + 4

= 3 + 4

=7

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