operatornameCot 12° Cot 102°+ operatornameCot 102° operatornameCot 66°+ operatornameCot 66° operatornameCot 12θ= ldots ldots ldots ldots

Question

operatornameCot 12° Cot 102°+ operatornameCot 102° operatornameCot 66°+ operatornameCot 66° operatornameCot 12θ= ldots ldots ldots ldots  (A) -1 (B) 2 (C) -2 (D) 1

Tardigrade Admin · Accepted Answer

cot 12° ⋅ cot 102°+ cot 102° ⋅ cot 66° + cot 66° ⋅ cot 12° = cot 12° ⋅ cot (90°+12°)+ cot (90°+12°) ⋅ cot 66° + cot 66° ⋅ cot 12° =- cot 12° ⋅ tan 12°- tan 12° ⋅ cot 66° + cot 66° ⋅ cot 12° =-1+ cot 66° ⋅ cot 12°- tan 12° =-1+ cot 66 ⋅ (1- tan 2 12°/ tan 12°) =-1+2 cot 66° ⋅ ( cot 2 12°-1/2 cot 12°) =-1+2 cot 66° cot 24° =-1+2 cot 66° ⋅ cot (90°-66°) =-1+2 cot 66° ⋅ tan 66° =2-1=1

Q. $Cot 1 2^{\circ} C o t 10 2^{\circ} + Cot 10 2^{\circ} Cot 6 6^{\circ} + Cot 6 6^{\circ} Cot 1 2^{θ} = \dots\dots\dots\dots$

$- 1$

$2$

$- 2$

$1$

Q. Cot12∘Cot102∘+Cot102∘Cot66∘+Cot66∘Cot12θ=…………

−1

2

−2

1

Q. $Cot 1 2^{\circ} C o t 10 2^{\circ} + Cot 10 2^{\circ} Cot 6 6^{\circ} + Cot 6 6^{\circ} Cot 1 2^{θ} = \dots\dots\dots\dots$

$- 1$

$2$

$- 2$

$1$