## CEBS95 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

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

2. CEBS95

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. CEBS95

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

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

6. CEBS95

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

7. Callisto

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

8. CEBS95

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. CEBS95

4 (1/2) = 2

11. Callisto

Yes.

12. winterfez

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

13. CEBS95

so, tan^2(60) = 3

14. Callisto

tan^2(60) = 3 <- Yes

15. winterfez

|dw:1355048071288:dw|

16. CEBS95

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. CEBS95

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

19. CEBS95

times 9 = 3 right?

20. Callisto

Yes.

21. CEBS95

8 sin ^2 (30) = 4 ?

22. CEBS95

no, i think it 8

23. CEBS95

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. CEBS95

2

26. CEBS95

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

27. winterfez

|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. winterfez

|dw:1355049643294:dw|

30. CEBS95

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. CEBS95

yes, with practice i will memorise the terms