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Question

Find the value of α for which the equality cos10o+sin10ocos10osin10o=cotα holds?

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Solution

Given,
cos10o+sin10ocos10osin10o=cotα.......(1)
Now,
cos10o+sin10ocos10osin10o
=cot10o+1cot10o1 [ Dividing both the numerator and the denominator by sin10o]
=cot10o.cot45o+1cot10ocot45o
=cot(45o10o)
=cot35o.
From (1) we've α=35o.

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