Question

which of them is possible cos a=7/5 sin a=13/12 sec a=4/5 tan a=41

Answer 1

Tan a = 41 is possible only.

because
0 ≤ sin a , cos a ≤ 1
and,
1 ≤ sec a ≤ ∞
hope this may help you..

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Answer 2

Cos a = 7/5
Adjacent side / Hypotenuse side = 7/5
Adjacent side = 7/5 × Hypotenuse side
Hypotenuse side can’t be less than any side. Hence it is impossible.

Sin a = 13/12
Opposite side / Hypotenuse side = 13/12
Opposite side = 13/12 × Hypotenuse side
Hypotenuse side can’t be less than any side. Hence it is impossible.

Sec a = 4/5
Hypotenuse side / Adjacent side = 4/5
Adjacent side = 5/4 × Hypotenuse sides
Hypotenuse side can’t be less than any side. Hence it is impossible.

Tan a = 41
Opposite side / Adjacent side = 41
In a right angled triangle adjacent side and opposite side can have any length. But their lengths should be less than Hypotenuse side length.
Hence Tan a = 41 is possible.