Trig Problem

Silverfalcon

Here is an interesting but easy challege.

Please do without using calculator.

$\sin (\cos^{-1} \frac {\sqrt 5}{5}) = \frac {a \cdot \sqrt b}{c}$

Where a,b, and c don't necessarily represent the different numbers.

Find $a+b+c$ .

**Posted:** Tue Feb 15, 2005 3:28 pm

sky9073 · Riemann Hypothesis Offline Joined: 26 Jan 2005 Posts: 455

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**Posted:** Tue Feb 15, 2005 4:01 pm

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oops

Ravi B

The problem should have imposed some restrictions on a, b, and c, such as they are all integers, b is square-free, and a and c are relatively prime.

**Posted:** Tue Feb 15, 2005 4:35 pm

Gyan

**Posted:** Wed Feb 16, 2005 1:29 pm

chenwb

it is implied that $\cos^{-1} x$ is the principal value...
on another note, verify $\tan^2 x+1=\sec^2 x$ .

**Posted:** Sun Feb 20, 2005 12:54 pm

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When all is said and done, more is said than done.

paladin8

**Posted:** Sun Feb 20, 2005 5:02 pm

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jli

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**Posted:** Tue Feb 22, 2005 1:58 pm

jli

$\tan^2 x+1=\sec^2 x$

$\frac{opposite^2}{adjacent^2}+\frac{adjacent^2}{adjacent^2}=\frac{hypotenus^2}{adjacent^2}$

$\frac{opposite^2+adjacent^2}{adjacent^2}=\frac{hypotenus^2}{adjacent^2}$

$\frac{hypotenus^2}{adjacent^2}=\frac{hypotenus^2}{adjacent^2}$

TADA!

**Posted:** Tue Feb 22, 2005 2:03 pm