Evaluate \frac{\tan 36}{ \cot 54}

Anonymous
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Step 1: Note down the given equation and known about the complimentary angles
EXAMPLE: \frac{\tan 36\degree}{ \cot 54\degree}
Step 2: Using the trigonometric ratio for complementary angles,
NOTE: we know that, \cot A = \tan (90\degree - A)
EXAMPLE: = \cot 54\degree = \tan (90\degree - 54\degree)
= \cot 54\degree = \tan 36 \degree.............(1)
Step 3: Insert the calculated values and solve for the unknown value.
EXAMPLE: = \frac{\tan 36\degree}{ \cot 54\degree}
= \frac{\tan 36\degree}{ \tan 36\degree} [since equation (1)]
= 1