Question

4/3tan square 30+ sin square 60 - 3cos square 60+ 3/4tan square 60-2tan square 45

Answer 1

here is ur answer
25/36 is the answer
hope it helps

Answer 2

$\frac{4}{3}\tan^230+\sin^2 60-3\cos^2 60+\frac{3}{4}\tan^2 60-2\tan^2 45=\frac{25}{36}$

Step-by-step explanation:

Given : Expression $\frac{4}{3}\tan^230+\sin^2 60-3\cos^2 60+\frac{3}{4}\tan^2 60-2\tan^2 45$

To find : Solve the expression ?

Solution :

$\frac{4}{3}\tan^230+\sin^2 60-3\cos^2 60+\frac{3}{4}\tan^2 60-2\tan^2 45$

Using trigonometric values,

$\sin 60=\frac{\sqrt3}{2}\\\\\cos 60=\frac{1}{2}\\\\\tan 30=\frac{1}{\sqrt3}\\\\\tan 45= 1\\\\\tan 60=\sqrt3$

Substitute the values,

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

$=\frac{4}{3}\times \frac{1}{3}+\frac{3}{4}-3\times \frac{1}{4}+\frac{3}{4}\times 3-2$

$=\frac{4}{9}+\frac{3}{4}-\frac{3}{4}+\frac{9}{4}-2$

$=\frac{4}{9}+\frac{9}{4}-2$

$=\frac{16+81-72}{36}$

$=\frac{25}{36}$

Therefore, $\frac{4}{3}\tan^230+\sin^2 60-3\cos^2 60+\frac{3}{4}\tan^2 60-2\tan^2 45=\frac{25}{36}$

#Learn more

3tan square 30 - tan square 60 +cosec 30 + tan 45 divided by cot square 45

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