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## anonymous 3 years ago tan^2(60) + 4cos^2(45) - 9tan^2(30) - 8sin^2(30) The answer is zero but why!? i need step by step solution please

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1. anonymous

why can't you just plug the whole thing into your calculator?

2. anonymous

because in the exam they already give you the answer, you have to do the procedure

3. Callisto

tan60 = $$\sqrt{3}$$ cos45 = $$\frac{1}{\sqrt2}$$ tan30 = $$\frac{1}{\sqrt3}$$ sin30 = 1/2 These are all special angles and you should remember them.

4. anonymous

yes i know them but i just continue to get 6 instead of 0

5. anonymous

I'm getting zero just fine though. note the squares.

6. anonymous

tan^2(60) = 3 ? 4cos^2(45) = 4 ?

7. Callisto

4cos^2(45) = 4 (1/2) = ...?

8. anonymous

my math base is not good, that's the reason i wrote step by step solution

9. Callisto

$cos45 =\frac{1}{\sqrt2}$$cos^245 =(\frac{1}{\sqrt2})^2 = \frac{1}{2}$$4cos45 =4(\frac{1}{2}) = ...?$

10. anonymous

4 (1/2) = 2

11. Callisto

Yes.

12. anonymous

$\frac{ \sin ^{2} (60)}{ \cos ^{2}(60)}+4\cos ^{2}(45)-9\frac{ \sin ^{2}(30) }{ \cos ^{2}(30) }-8\sin ^{2}(30)$

13. anonymous

so, tan^2(60) = 3

14. Callisto

tan^2(60) = 3 <- Yes

15. anonymous

|dw:1355048071288:dw|

16. anonymous

i found in my book that cos 45 = $\frac{ \sqrt{2} }{ 2}$

17. Callisto

$\frac{1}{\sqrt2}=\frac{1}{\sqrt2}\times \frac{\sqrt2}{\sqrt2}=\frac{\sqrt2}{\sqrt2^2} = \frac{\sqrt2}{2}$ Just rationalization.

18. anonymous

9tan^2(30) = $\tan( 30) = \frac{ \sqrt{3} }{ 3 } ; \tan ^{2}(30) = 3/9 = 1/3$

19. anonymous

times 9 = 3 right?

20. Callisto

Yes.

21. anonymous

8 sin ^2 (30) = 4 ?

22. anonymous

no, i think it 8

23. anonymous

9tan^2(30) - 8sin^2(30) = 3 - 8 = -5, at the end that will give me 5- (-5) that equals 10

24. Callisto

8 sin ^2 (30) = 8 (1/2)^2 = 8 (1/4) = ...

25. anonymous

2

26. anonymous

still, 3-2 = 1, 5-1 = 4

27. anonymous

|dw:1355049445375:dw| look at this one to see how i get 0

28. Callisto

tan^2(60) + 4cos^2(45) - 9tan^2(30) - 8sin^2(30) tan^2(60) = $$\sqrt3^2$$ = ... 4cos^2(45) = 4$$(\frac{1}{\sqrt2})^2$$ = 4(1/2) = ... - 9tan^2(30) = -9 $$(\frac{1}{\sqrt3})^2$$ = -9 (1/3) = ... - 8sin^2(30) = -8 (1/2)^2 = -8 (1/4) = ... Sum up the four answers.

29. anonymous

|dw:1355049643294:dw|

30. anonymous

zero! nice thanks calisto

31. Callisto

You're welcome :)

32. Callisto

| 30 | 45 | 60 ------------------------------------ sin | $$\frac{1}{2}$$ | $$\frac{1}{\sqrt2} /\frac{\sqrt2}{2}$$ | $$\frac{\sqrt3}{2}$$ ------------------------------------ cos | $$\frac{\sqrt3}{2}$$ | $$\frac{1}{\sqrt2} /\frac{\sqrt2}{2}$$ | $$\frac{1}{2}$$ ------------------------------------ tan | $$\frac{1}{\sqrt3} /\frac{\sqrt3}{3}$$ | 1 | $$\sqrt{3}$$

33. Callisto

Memorize the table..

34. anonymous

yes, with practice i will memorise the terms

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