Question

√3+cot50+tan80=√3.cot50.tan80​

Answer 1

80+40=120

$\tan(80 + 40 )= \tan(120) )$

Answer 2

Hence Proved.

Step-by-step explanation:

Given,

$\sqrt{3} +cot50+tan80=\sqrt{3} .cot50. tan80$

∴ $80+40=120$

Take $tan$ on both sides,

⇒$tan(80+40)=tan120$

⇒$\frac{tan80+tan40}{1-tan40.tan80} =-\sqrt{3}$

⇒$-\sqrt{3} +\sqrt{3}tan40.tan80=tan40+tan80$

⇒$\sqrt{3}.tan40.tan80=\sqrt{3}+ tan40+tan80$

⇒$\sqrt{3} .cot50. tan80=\sqrt{3} +cot50+tan80$ (∵ $tan(90-50)=cot50$ )

∴$\sqrt{3} +cot50+tan80=\sqrt{3} .cot50. tan80$

Hence Proved.