Question

State the value of


`\tan(60°) + \cot(60°)`
rationalise the denominator if needed !

thankyou ~​

Answer 1

`tan(60)+cot60)\\√(3) +(1)/(√(3) ) \\(3+1)/(√(3) ) \\(4)/(√(3) ) *(√(3) )/(√(3) ) \\(4√(3) )/(3)`

Hope it will help you a lot.

Explanation:

Answer 2

`(4\sqrt3)/(3)`

Explanation:

`\pink{\frak{Given }}\Bigg\{ \sf \tan(60^o) + \cot(60^o)`

And we need to find out the value of given expression . As we know that the value of ,

`\sf \longrightarrow tan 60^o = \sqrt3`

And ,

`\sf \longrightarrow cot 60^o = (1)/(tan60^o)=(1)/(\sqrt3)`

Substituting the values in the given expression ,

`\sf \longrightarrow tan 60^o + cot 60^o\\`

`\sf \longrightarrow \sqrt3 +(1)/(\sqrt3)\\`

Take LCM as √3 and simplify ,

`\sf \longrightarrow ((\sqrt3)(\sqrt3) +1)/(\sqrt3)\\`

Simplify ,

`\sf \longrightarrow (3+1)/(\sqrt3)=(4)/(\sqrt3)`

Rationalize the denominator by multiplying numerator and denominator by √3 .

`\sf \longrightarrow ((4)(\sqrt3))/((\sqrt3)(\sqrt3))`

Simplify by multiplying ,

`\sf \longrightarrow \boxed{\bf (4\sqrt3)/(3)}`