Question

(iii) tan 15° + cot 15° = 4​

Answer 1

Given Tan 15 + cot 15

= sin 15/cos 15 + cos 15/sin 15

= (sin^2 15 + cos^2 15)/sin 15 cos 15

= 1/1/2 sin (15 + 15) - sin(15 - 15)

= 1/(1/2 sin 30)

= 2/sin 30

= 2/ (1/2)

= 4.

LHS = RHS.

Answer 2

Step-by-step explanation:

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