Question 198700
It's really "theta" not "phata", but I like "phata" better!  It's cute!  I can't make a "theta" on here, so I'll use P for "phata".

I need help to rewrite each expression in terms of cosP. Then simplify.

1. {{{2*SinP*CosP*CotP}}}
   
Change the {{{CotP}}} to {{{CosP/SinP}}} 

{{{2*SinP*CosP*(CosP/SinP)}}}

Cancel the {{{SinP}}}'s.

{{{2*cross(SinP)*CosP*(CosP/cross(SinP))}}}

{{{2*Cos^2P}}}


2. 1 + cot phata divided by cot phata ( sin phata+ cos phata)

{{{(  (1+CotP)/CotP  )(SinP+CosP) }}}

Change both {{{CotP}}}'s to {{{CosP/SinP}}} 

{{{(  (1+CosP/SinP)/(CosP/SinP)  )(SinP+CosP) }}}

Change the {{{1}}} to {{{SinP/SinP}}}

{{{(  (SinP/SinP+CosP/SinP)/(CosP/SinP)  )(SinP+CosP) }}}

{{{ (((SinP+CosP)/SinP)/(CosP/SinP) )(SinP+CosP) }}}

Invert and multiply:

{{{((  (SinP+CosP)/SinP)*(SinP/CosP)  )(SinP+CosP) }}}

Cancel the {{{SinP}}}'s

{{{( ( (SinP+CosP)/cross(SinP))*(cross(SinP)/CosP))*(SinP+CosP)}}}

{{{ ( (SinP+CosP)/CosP  )(SinP+CosP) }}}

{{{ ( (SinP+CosP)/CosP  )((SinP+CosP)/1) }}}

{{{ (SinP+CosP)^2/CosP}}}

Now since {{{Sin^2P+Cos^2P=1}}} solved for {{{SinP}}} is
           {{{SinP = ""+-sqrt(1-Cos^2P)}}}

{{{ (""+-sqrt(1-Cos^2P)+CosP)^2/CosP}}}   





3. cos square root of 4 phata - sin square root of 4 phata + sin squareroot of 2 phata.