cot A = 1/tan A = 1/(1/√3) = √3 — (1)
Using Trigonometric Identity:
1 + tan²A = sec²A
1 + (1/√3)² = sec²A
sec²A = 1 + 1/3 = 4/3
sec A = +√(4/3) = +2/√3
or sec A = -2/√3 (neglecting this value as A is acute angle)
Therefore, sec A = 2/√3
Using Trigonometric Identity:
1 + cot²A = cosec²A
1 + (√3)² = cosec²A
4 = cosec²A
cosec A = 2
Again, sin A = 1/cosec A = 1/2
sin A = 1/2
cos A = 1/sec A = 1/(2/√3) = √3/2
Thus:
sin A = 1/2
cos A = √3/2
cot A = √3
cosec A = 2
sec A = 2/√3
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