Question

tan 20 tan 80 cot 50=√3​

Answer 1

Answer:

hope it can helpful to you

Answer 2

Step-by-step explanation:

Consider the provided information.

tan 20 tan 80 cot 50=√3​

Consider the left hand side.

$\tan 20^{\circ} \tan 80^{\circ} \cot 50^{\circ}$

$\tan ( 50 - 30 )^{\circ} \times \tan (50 + 30)^{\circ} \times \frac{1}{\tan 50^{\circ}}$

Use the identity:

$tan(A-B)=\frac{tan A- tan B}{1+tan A.tan B}\\tan(A+B)=\frac{tan A+tan B}{1-tan A.tan B}$

⇒$\frac{ tan 50^{\circ}-tan 30^{\circ}}{1+tan 56^{\circ}\times tan 30^{\circ}}\times \frac{ tan 50^{\circ}+tan 30^{\circ}}{1-tan 56^{\circ}\times tan 30^{\circ}} \times \frac{1}{tan 50^{\circ}}$

⇒$\frac{ tan 50^{\circ}-\frac{1}{\sqrt{3}}}{1+tan 56^{\circ}\times\frac{1}{\sqrt{3}}}\times \frac{ tan 50^{\circ}+\frac{1}{\sqrt{3}}}{1-tan 50^{\circ}\times\frac{1}{\sqrt{3}}}\times \frac{1}{tan 50^{\circ}}$

⇒$\frac{3 tan^250^{\circ} - 1 }{3 tan 50^{\circ}-tan^350^{\circ}}$

⇒$-cot (150^{\circ})$

⇒$cot 30^{\circ}\\\sqrt{3}$

Hence, proved

#Learn more

Prove this trignometric identity please​

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