tan15°.+cot15°=4 prove that
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HEY DEAR ...✌
____________________________
tan 15 = tan (45 - 30)
.. .. tan 60 - tan 45
= -------------------------
.. .1 + tan 60 tan 45
.. .. √3 - 1
= ------------
.. .. 1 + √3
.. .. √3 - 1
= ------------
.. .. √3 + 1
cot 15 = 1 / tan 15
.. .. √3 + 1
= ------------
.. .. √3 - 1
tan 15 - cot 15
.. .. √3 - 1 .. .. .. .. √3 + 1
= ------------ .. + .. --------------
.. .. √3 + 1 .. .. .. ..√3 - 1
.. .. (√3 - 1)² + (√3 - 1)²
= --------------------------------
.. .. .. .. ..3 - 1
.. .. (3 - 2√3 + 1) + (3 + 2√3 + 1)
= ----------------------------------------...
.. .. .. .. .. .. .. 3 - 1
= 8/2 = 4
HOPE , IT HELPS ... ✌
____________________________
tan 15 = tan (45 - 30)
.. .. tan 60 - tan 45
= -------------------------
.. .1 + tan 60 tan 45
.. .. √3 - 1
= ------------
.. .. 1 + √3
.. .. √3 - 1
= ------------
.. .. √3 + 1
cot 15 = 1 / tan 15
.. .. √3 + 1
= ------------
.. .. √3 - 1
tan 15 - cot 15
.. .. √3 - 1 .. .. .. .. √3 + 1
= ------------ .. + .. --------------
.. .. √3 + 1 .. .. .. ..√3 - 1
.. .. (√3 - 1)² + (√3 - 1)²
= --------------------------------
.. .. .. .. ..3 - 1
.. .. (3 - 2√3 + 1) + (3 + 2√3 + 1)
= ----------------------------------------...
.. .. .. .. .. .. .. 3 - 1
= 8/2 = 4
HOPE , IT HELPS ... ✌
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