Question

find the value of 4 tan 45°+root 3 cot 60°+tan 30° cot 45°​

Answer 1

may be 2/ root 3 us the answerr

Answer 2

Answer:

4tan45+3cot60+3sin260+tan30cot45=43293+4

Step-by-step explanation:

Given : Expression 4\tan 45+\sqrt{3}\cot 60+3\sin^2 60+\tan 30\cot 454tan45+3cot60+3sin260+tan30cot45

To find : Solve the expression ?

Solution :

Expression 4\tan 45+\sqrt{3}\cot 60+3\sin^2 60+\tan 30\cot 454tan45+3cot60+3sin260+tan30cot45

Using trigonometric values,

\sin 60=\frac{\sqrt3}{2}sin60=23

\tan 45=1tan45=1

\tan 30=\frac{1}{\sqrt3}tan30=31

\cot 45=1cot45=1

\cot 60=\frac{1}{\sqrt3}cot60=31

Substitute the values,

=4(1)+\sqrt{3}(\frac{1}{\sqrt3})+3(\frac{\sqrt3}{2})^2+(\frac{1}{\sqrt3})(1)=4(1)+3(31)+3(23)2+(31)(1)

=4+1+3(\frac{3}{4})+\frac{1}{\sqrt3}=4+1+3(43)+31

=5+\frac{9}{4}+\frac{1}{\sqrt3}=5+49+31

=\frac{20\sqrt3+9\sqrt3+4}{4\sqrt3}=43203+93+4

=\frac{29\sqrt3+4}{4\sqrt3}=43293+4

Therefore, 4\tan 45+\sqrt{3}\cot 60+3\sin^2 60+\tan 30\cot 45=\frac{29\sqrt3+4}{4\sqrt3}4tan45+3cot60+3sin260+tan30cot45=43293+4

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