Question

4 tan 45 + √3 Cot 60 + 3 sin² 60 + tan 30 cot 45

Answer 1

Step-by-step explanation:

4+3+3×3/4+1/√3=7+9/4+1/√3

37/4+1/√3

Answer 2

$4\tan 45+\sqrt{3}\cot 60+3\sin^2 60+\tan 30\cot 45=\frac{29\sqrt3+4}{4\sqrt3}$

Step-by-step explanation:

Given : Expression $4\tan 45+\sqrt{3}\cot 60+3\sin^2 60+\tan 30\cot 45$

To find : Solve the expression ?

Solution :

Expression $4\tan 45+\sqrt{3}\cot 60+3\sin^2 60+\tan 30\cot 45$

Using trigonometric values,

$\sin 60=\frac{\sqrt3}{2}$

$\tan 45=1$

$\tan 30=\frac{1}{\sqrt3}$

$\cot 45=1$

$\cot 60=\frac{1}{\sqrt3}$

Substitute the values,

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

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

$=5+\frac{9}{4}+\frac{1}{\sqrt3}$

$=\frac{20\sqrt3+9\sqrt3+4}{4\sqrt3}$

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

Therefore, $4\tan 45+\sqrt{3}\cot 60+3\sin^2 60+\tan 30\cot 45=\frac{29\sqrt3+4}{4\sqrt3}$

#Learn more

Tan (45+A)/tan(45-A)​

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