1. ## cos35sin55 + cos55sin35

ok the answer 1 apparently because i went on hotmath.com and it explained it like this

cos35sin55 + cos55sin35

sin^2 55 + cos ^2 35 =1

ok i understand that

but cos35 and sin 55 are equal and so are cos55 and sin35

so i thought it would be like...1 + 1...i dont understand why that isn't correct.

2. Originally Posted by desperate_on_sunday_night
ok the answer 1 apparently because i went on hotmath.com and it explained it like this

cos35sin55 + cos55sin35

sin^2 55 + cos ^2 35 =1

ok i understand that

but cos35 and sin 55 are equal and so are cos55 and sin35

so i thought it would be like...1 + 1...i dont understand why that isn't correct.
huh?

the original expression is the addition formula for sine:

cos35sin55 + cos55sin35 = sin(55 + 35) = sin90 = 1

neither sin^2 (55) nor cos^2 (35) are 1

any questions?

3. Originally Posted by desperate_on_sunday_night
ok the answer 1 apparently because i went on hotmath.com and it explained it like this

cos35sin55 + cos55sin35

sin^2 55 + cos ^2 35 =1

ok i understand that

but cos35 and sin 55 are equal and so are cos55 and sin35

so i thought it would be like...1 + 1...i dont understand why that isn't correct.
I think what the poster meant was

$\cos(55)=\sin(90-55)=\sin(35)$

and $\sin(55)=\cos(90-55)=\cos(35)$

Giving us

$\sin^2(55)+\cos^2(55)=1$

4. Hello, desperate_on_sunday_night!

ok the answer 1 apparently because i went on hotmath.com and it explained it like this

$\cos35\sin55 + \cos55\sin35$

$\sin^2\!55 + \cos^2\!35 \:=\:1$

ok i understand that . . . . you do?
If that's all they wrote, very sloppy!!

We're expected to visualize this right triangle . . .
Code:
                        *
*  *
c   * 55° *
*        * a
*           *
* 35°          *
*  *  *  *  *  *  *
b

$\begin{array}{cccccc}\text{We see that:} &\cos35 & = & \frac{b}{c} &=& \sin 55^o \\
\text{and that:} & \sin35 &=& \frac{a}{c} &=& \cos55^o\end{array}$

. We have: . $\underbrace{\cos35}_{\downarrow}\sin55 + \cos55\underbrace{\sin35}_{\downarrow}$
Substitute: . $\overbrace{\sin55}\sin55 + \cos55\overbrace{\cos55} \;\;=\;\;\sin^2\!55 + \cos^2\!55 \;\;=\;\;1$

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# sin35cos55 cos35sin55

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