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Question
Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°
tan 65° + cot 49°
Solution
We know `tan (90^@ - theta) = cot theta` and `cot(90^@ - theta) = tan theta`. So
`tan 65° + cot 49° = tan(90^@ - 25^@) + cot 90^@ (90^@ - 41^@)`
`= cot 25^@ + tan 41^@`
Thus the desired expression is `= cot 25^@ + tan 41^@`
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