Question

the value of tan 75° - cot ​

Answer 1

Answer:

MATHS

The value of tan75

∘

−cot75

∘

=

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ANSWER

tan75°−cot75°

⇒ Now, tan75°=tan(45°+30°)

=

1−tan45°tan30°

tan45°+tan30°

[∵tan(A+B)=

1−tanAtanB

tanA+tanB

]

=

1−

3

1

1+

3

1

⇒tan75°=

3

−1

3

+1

cot75°=

tan75°

1

=

3

+1

3

−1

So, tan75°−cot75°=

3

−1

3

+1

−

3

+1

3

−1

=

(

3

−1)(

3

+1)

(

3

+1)

2

−(

3

−1)

2

=

3−1

3+1+2

3

−3−1+2

3

=

2

4

3

=2

3

Hence, the answer is 2

3

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