Question 1086800
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(cos˛x + sin˛x)/(cot˛x - cosec˛x)

(cos˛x + sin˛x) ÷ (cot˛x - cosec˛x)

Use the identity 

              cos˛<font face="symbol">q</font> + sin˛<font face="symbol">q</font> = 1

1 ÷ (cot˛x - cosec˛x)

Use the identities
 
              cot<font face="symbol">q</font> = cos<font face="symbol">q</font>/sin<font face="symbol">q</font> and
              cosec<font face="symbol">q</font> = 1/sin<font face="symbol">q</font>

1 ÷ (cos˛x/sin˛x - 1/sin˛x)

1 ÷ (cos˛x - 1)/sin˛x

Use the identity again

              cos˛<font face="symbol">q</font> + sin˛<font face="symbol">q</font> = 1, solved for cos˛<font face="symbol">q</font>
              cos˛<font face="symbol">q</font> = 1 - sin˛<font face="symbol">q</font> 

1 ÷ (1 - sin˛x - 1)/sin˛x

1 ÷ -sin˛x/sin˛x

1 ÷ -1

-1

Edwin</pre></font></b>