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.