Question

Find tan 15° and hence show that tan 15º+cot 15° = 4​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

tan 15° = tan (45° - 30°)

tan 45° - tan 30°

= ---------------------------

1 + tan 45° tan 30°

1 - 1/√3

= -----------------

1 + (1) (1/√3)

1 - 1/√3

= -----------------

1 + 1/√3

= √3 - 1 / √3 + 1

rationalising the denominator, we get

tan 15° = 2 - √3

similarly cot 15° = 2 + √3

.•. tan 15º+cot 15° = 2 - √3 + 2 + √3 = 2 + 2 = 4