If sin 31° = α, then find the value of cot 59°.

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Given sin 31° = α.

We need to find cot 59°.

Step 1: Use the complementary angle identity:
Since 59° = 90° - 31°, cot 59° = tan 31°.

Step 2: Express tan 31° in terms of sin 31° (α):
We know tan θ = sin θ / cos θ.

Step 3: Find cos 31°:
cos 31° = √(1 - sin² 31°) = √(1 - α²).

Step 4: Therefore,
tan 31° = sin 31° / cos 31° = α / √(1 - α²).

Since cot 59° = tan 31°, the value is α / √(1 - α²).

Hence, option 2 is correct.

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