The value of tan75° - cot75° is equal to

Question

The value of tan75° - cot75° is equal to (A) 2√3 (B) 2+√3 (C) 2-√3 (D) 1

Tardigrade Admin · Accepted Answer

tan75°-cot75°=tan(45°+30°)-cot(45°+30°) =(tan 45°+tan 30°/1-tan 45° tan 30°)-(cot 45° cot 30°-1/cot 45°+cot 30°) =(1+(1/√3)/1-(1)√3)-(√3-1/1+√3) =((√3+1)/(√3-1))-(√3-1/√3+1) =((3+1+2√3)/3-1)-((3+1-2√3)/3-1) =(4√3/2)=2√3

Q. The value of $t an 7 5^{\circ} - co t 7 5^{\circ}$ is equal to

$23$

$2 + 3$

$2 - 3$

$1$

Q. The value of tan75∘−cot75∘ is equal to

23​

2+3​

2−3​

1

tan75∘−cot75∘=tan(45∘+30∘)−cot(45∘+30∘) =1−tan45∘tan30∘tan45∘+tan30∘​−cot45∘+cot30∘cot45∘cot30∘−1​ =1−3​1​1+3​1​​−1+3​3​−1​ =(3​−1)(3​+1)​−3​+13​−1​ =3−1(3+1+23​)​−3−1(3+1−23​)​ =243​​=23​

Q. The value of $t an 7 5^{\circ} - co t 7 5^{\circ}$ is equal to

$23$

$2 + 3$

$2 - 3$

$1$