Sec square 75 degree + cot square 15 degree

(6 +√3) / (2 - √3).

Step-by-step explanation:

sec 75 = 1/cos 75

cos 75 = cos45cos30 - sin45sin30

= 1/√2 * √3/2 - 1/√2 * 1/2

= (√3 - 1 )/ 2√2.

cos^2 75

=  (√3 - 1 )^2 / (2√2)^2

= (3 - 2√3 + 1 / 8

= (2 - √3) / 4

So sec^2 75  = 4 / (2 - √3)

tan 15 =  tan (45 - tan 30)

= tan 45 - tan 30 / 1 + tan45 tan30

= ( 1 - √3/3 ) / (1 + 1 * √3 / 3)

= (3 - √3) / (3 + √3)

tan^2 15 =  (9 - 6√3 + 3) / (9 + 6√3 + 3)

= 12 - 6√3  (12 + 6√3)

=  2 - √3 / 2 + √3

So cot^2 15 = (2 + √3) / (2 - √3)

Finally sec^2 75 + cot^2 15

= 4 / (2 - √3) +  (2 + √3) / (2 - √3)

= (6 +√3) / (2 - √3)

Step-by-step explanation:

but

You work for the final answer.

it should be described as a proper fraction.