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anonymous
 one year ago
how do i verify
cot (x pi/2)=tanx
i dont know how to do this so pls be patient with me!
anonymous
 one year ago
how do i verify cot (x pi/2)=tanx i dont know how to do this so pls be patient with me!

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jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1hmmm \(\bf cot\left( x\cfrac{\pi }{2} \right) = tan(x)?\)

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1hmmm what's the \(\bf cos\left(\frac{\pi }{2} \right)\quad and \quad sin\left(\frac{\pi }{2} \right)\)

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1ehehh, what are, check your Unit Circle, the \(\bf cos\left(\frac{\pi }{2} \right)\quad and \quad sin\left(\frac{\pi }{2} \right)?\)

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.11/2 and 0? check your unit circle closer

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0(0,1) ? i dont know i just started

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1hmmm, well, \(\bf cos\left(\frac{\pi }{2} \right)=0\quad and \quad sin\left(\frac{\pi }{2} \right)=1\) so we know that much

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how is that relevant?

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1\(\bf cot\left( x\frac{\pi }{2} \right)\implies \cfrac{cos\left( x\frac{\pi }{2} \right)}{sin\left( x\frac{\pi }{2} \right)} \\ \quad \\ \cfrac{cos(x)cos\left(\frac{\pi }{2} \right)+sin(x)sin\left(\frac{\pi }{2} \right)}{sin(x)cos\left(\frac{\pi }{2} \right)cos(x)sin\left(\frac{\pi }{2} \right)} \\ \quad \\ \cfrac{cos(x)\cdot {\color{brown}{ 0}}+sin(x)\cdot {\color{brown}{ 1}}}{sin(x)\cdot {\color{brown}{ 0}}cos(x)\cdot {\color{brown}{ 1}}}\implies \cfrac{sin(x)}{cos(x)}\implies ?\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wait wait wait how did you get that huge second fraction

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1recall \(\bf \textit{Sum and Difference Identities} \\ \quad \\ sin({\color{brown}{ \alpha}}  {\color{blue}{ \beta}})=sin({\color{brown}{ \alpha}})cos({\color{blue}{ \beta}}) cos({\color{brown}{ \alpha}})sin({\color{blue}{ \beta}}) \\ \quad \\ cos({\color{brown}{ \alpha}}  {\color{blue}{ \beta}})= cos({\color{brown}{ \alpha}})cos({\color{blue}{ \beta}}) + sin({\color{brown}{ \alpha}})sin({\color{blue}{ \beta}})\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so sin/cos=tan because tan=sin/cos right

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1\(\bf \textit{Sum and Difference Identities} \\ \quad \\ sin({\color{brown}{ x}}  {\color{blue}{ \frac{\pi }{2}}})=sin({\color{brown}{ x}})cos({\color{blue}{ \frac{\pi }{2}}}) cos({\color{brown}{ x}})sin({\color{blue}{ \frac{\pi }{2}}}) \\ \quad \\ cos({\color{brown}{ x}}  {\color{blue}{ \frac{\pi }{2}}})= cos({\color{brown}{ x}})cos({\color{blue}{ \beta}}) + sin({\color{brown}{ x}})sin({\color{blue}{ \frac{\pi }{2}}})\)

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1\(\bf \cfrac{cos(x)\cdot {\color{brown}{ 0}}+sin(x)\cdot {\color{brown}{ 1}}}{sin(x)\cdot {\color{brown}{ 0}}cos(x)\cdot {\color{brown}{ 1}}}\implies \cfrac{sin(x)}{cos(x)}\implies \cfrac{sin(x)}{1\cdot cos(x)} \\ \quad \\ \cfrac{1}{1}\cdot \cfrac{sin(x)}{cos(x)}\implies  \cfrac{sin(x)}{cos(x)}\implies tan(x)\)
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