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Question
The value of tan 25° tan 10° tan 80° tan 65° is ______.
Fill in the Blanks
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Solution
The value of tan 25° tan 10° tan 80° tan 65° is 1.
Explanation:
tan (90° – θ) = cot θ, so tan 25° · tan 65° = tan 25° · tan (90° − 25°) = 1
And tan 10° · tan 80° = tan 10° · tan (90° – 10°) = 1
Therefore the whole product = 1.
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