If cos teta_sin teta=root 2 sin teta , then prove that cos teta +sin teta = =root 2 cos teta

Asked by Sai Seravan Bodipudi | 8th Dec, 2014, 08:07: PM

Expert Answer:

C o n s i d e r space t h e space g i v e n space e q u a t i o n space cos theta minus sin theta equals square root of 2 sin theta : cos theta minus sin theta equals square root of 2 sin theta rightwards double arrow space cos theta equals sin theta plus square root of 2 sin theta rightwards double arrow space cos theta equals open parentheses square root of 2 plus 1 close parentheses sin theta rightwards double arrow open parentheses square root of 2 plus 1 close parentheses sin theta equals space cos theta rightwards double arrow sin theta equals space fraction numerator cos theta over denominator open parentheses square root of 2 plus 1 close parentheses end fraction rightwards double arrow sin theta equals space fraction numerator open parentheses 2 minus 1 close parentheses cos theta over denominator open parentheses square root of 2 plus 1 close parentheses end fraction rightwards double arrow sin theta equals space fraction numerator open parentheses 2 minus 1 close parentheses over denominator open parentheses square root of 2 plus 1 close parentheses end fraction cross times cos theta rightwards double arrow sin theta equals space fraction numerator open parentheses square root of 2 minus 1 close parentheses cross times open parentheses square root of 2 plus 1 close parentheses over denominator open parentheses square root of 2 plus 1 close parentheses end fraction cross times cos theta space space space space space space open square brackets because a squared minus b squared equals open parentheses a plus b close parentheses open parentheses a minus b close parentheses close square brackets rightwards double arrow sin theta equals space open parentheses square root of 2 minus 1 close parentheses cross times cos theta space space rightwards double arrow sin theta equals square root of 2 cross times cos theta minus 1 cross times cos theta rightwards double arrow cos theta plus sin theta equals square root of 2 cos theta H e n c e space p r o v e d.

Answered by Vimala Ramamurthy | 9th Dec, 2014, 10:28: AM