# Trigonometry Expression

Is $(\sin \phi)^2$ is equal to $\sin^2\phi$?

Can any one tell what is the ans for the below expression

$\sin^260$ + $\cos^260$ + $\tan^245$ + $\sec^260$ - $\csc^260$

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"wats" should be "what's" (or "what is"). – ShreevatsaR Jan 31 '11 at 10:02
I vote to close this question since it is too localized and it involves only elementary arithmetic. – user17762 Jan 31 '11 at 10:06

## 2 Answers

($sin \phi$)^2 is equal to $sin^2\phi$.

$sin^260$ + $cos^260$ + $tan^245$ + $sec^260$ - $cosec^260$

The trick to that is to use a few trigonometric identities.

$\sin^2\theta + \cos^2\theta = 1$
$\tan 45 = 1$

The value of $\cos 60$ is $\frac{1}{2}$, so $\sec^260$ will evaluate to 4. The value of $\sin 60$ is $\sqrt{\frac{3}{4}}$, so $\csc^260$ will evaluate to $\frac{4}{3}$.

Adding it all up you have $1 + 1 + 4 - \frac{4}{3} = \frac{14}{3}$

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typo: $\csc^2 60^\circ$ will evaluate to $\frac{4}{3}$ – Américo Tavares Jan 31 '11 at 20:52
My apologies, I edited the answer to reflect that. I was copying and pasting the math syntax and forgot to change that – Varun Madiath Jan 31 '11 at 21:18

Yes, $sin^2\phi$ is by definition $(sin\phi)^2$. The answer to the last question is: you can calculate sin(60), cos(60) and tan(45) just using Pythagoras. A hint for the first two of these: draw a right angled triangle with one angle of 60 degrees. What is the third angle? Can you exploit the symmetry?

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@ Alex bartel : Sorry, typo... edited in – Pramodh Jan 31 '11 at 8:17