Question 549270
Prove that :
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1. {{{(cscA-1)/(cscA+1)}}} = {{{(1-sinA)/(1+sinA)}}}

  {{{(cscA-1)}}}÷{{{(cscA+1)}}}

{{{( 1/sinA-1 )}}}÷{{{( 1/sinA+1)}}}

{{{( 1/sinA-sinA/sinA )}}}÷{{{( 1/sinA+sinA/sinA)}}}

{{{ (1-sinA)/sinA }}}÷{{{ (1+sinA)/sinA}}}

{{{ (1-sinA)/sinA }}}×{{{ sinA/(1+sinA)}}}

{{{ (1-sinA)/cross(sinA) }}}×{{{ cross(sinA)/(1+sinA)}}}

{{{(1-sinA)/(1+sinA)}}}


2. {{{(secA/cscA)}}} + {{{(sinA/cosA)}}} = {{{2tanA}}}

   {{{secA}}}÷{{{cscA}}} + {{{(sinA/cosA)}}}

   {{{1/cosA}}}÷{{{1/sinA)}}} + {{{(sinA/cosA)}}}
    
   {{{1/cosA}}}×{{{sinA/1)}}} + {{{(sinA/cosA)}}}

   {{{(sinA/cosA)}}} + {{{(sinA/cosA)}}}

   {{{tanA}}} + {{{tanA}}}

   {{{2tanA}}}


3. {{{(1+sinA)/(1-sinA)}}} = {{{(cscA+1)/(cscA-1)}}}

You can do that one by substituting {{{1/sinA}}} for {{{cscA}}}
It's similar to the first one.

4. {{{sinA/(sinA-cosA)}}} = {{{1/(1-cotA)}}}
                    = {{{1}}}÷{{{1-cotA}}}
                    = {{{1}}}÷{{{1-cosA/sinA}}} 
                    = {{{1}}}÷{{{sinA/sinA-cosA/sinA}}}
                    = {{{1}}}÷{{{(sinA-cosA)/sinA}}}
                    = {{{1}}}×{{{sinA/(sinA-cosA)}}}                 
                    = {{{sinA/(sinA-cosA)}}}

5. {{{(tanA+cotA)/tanA}}} = {{{csc^2A}}}
   {{{tanA/tanA+cotA/tanA}}} 
   {{{1+cotA/tanA}}} 
   {{{1}}} + {{{cotA/tanA}}}
   {{{1}}} + {{{cotA}}}÷{{{tanA}}}
   {{{1}}} + {{{cotA}}}÷{{{1/cotA}}}
   {{{1}}} + {{{cotA}}}×{{{cotA/1}}}
   {{{1}}} + {{{cotA}}}×{{{cotA}}}  
   {{{1}}} + {{{cot^2A}}}
   {{{csc^2A}}}

Edwin</pre>