Question

prove tan 75 +cot 75=4

Answer 1

Answer:

Step-by-step explanation:

tan75°=tan(30°+45°)

=(tan30°+tan45°)/(1-tan30°tan45°)

={(1/√3)+1}/{1-(1/√3)(1)}

=(√3+1)/(√3-1)

So,cot75°=1/tan75°

=(√3-1)/(√3+1)

Then,tan75°+cot75°={(√3+1)2+(√3-1)2}/{(√3)2-(1)2}

=4

Answer 2

The value of tan 75 and cot 75 is 4.

Given:

tan 75 + cot 75

To Find:

Value of tan 75+ cot 75

Solution:

tan 75= 2+√3

cot 75 = 2-√3

tan 75+cot 75 = 2+√3+2-√3

tan 75+ cot 75 = 4.

Hence, the value of tan 75+ cot 75 is 4.

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