REDUCE TO SINE OR COSINE OF A SINGLE EXPRESSION 
  COS A - SIN A

Asked by dalbirgolagarh | 16th Aug, 2016, 10:27: PM

Expert Answer:

begin mathsize 24px style Using space the space formula space that colon
acosx plus bsinx space equals space Rcos left parenthesis straight x space minus space straight p right parenthesis
where space straight p space equals arctan left parenthesis straight b over straight a right parenthesis
and space straight R space equals space square root of straight a squared plus straight b squared end root
The space given space question space has space straight a equals space 1 space space and space straight b equals space minus 1
Hence space straight p space equals arctan left parenthesis fraction numerator negative 1 over denominator 1 end fraction right parenthesis space equals space arctan left parenthesis negative 1 right parenthesis space equals negative 45 to the power of straight o
and space straight R equals square root of left parenthesis 1 right parenthesis squared plus space left parenthesis negative 1 right parenthesis squared end root space space equals square root of 1 plus 1 end root space equals square root of 2
cos space straight A minus space sin space straight A space equals space square root of 2 cos left parenthesis straight A minus left parenthesis negative 45 to the power of straight o right parenthesis right parenthesis space equals space square root of 2 cos left parenthesis straight A plus 45 to the power of straight o right parenthesis end style

Answered by Tripti Agrawal | 17th Aug, 2016, 11:17: AM