Prove the following

Asked by Apoorva | 14th Jun, 2017, 08:39: PM

Expert Answer:

                                                                                                                                                                                begin mathsize 16px style straight g right parenthesis
cos space straight theta minus sin space straight theta equals square root of 2 sin space straight theta
rightwards double arrow open parentheses cos space straight theta minus sin space straight theta close parentheses squared equals open parentheses square root of 2 sin space straight theta close parentheses squared
rightwards double arrow cos squared straight theta plus sin squared straight theta minus 2 sin space straight theta space cos space straight theta equals 2 sin squared space straight theta
rightwards double arrow sin squared straight theta plus 2 sin space straight theta space cos space straight theta equals cos squared space straight theta
rightwards double arrow sin squared straight theta plus 2 sin space straight theta space cos space straight theta plus cos squared space straight theta equals 2 cos squared space straight theta
rightwards double arrow left parenthesis sin space straight theta plus cos space straight theta right parenthesis squared equals 2 cos squared straight theta
rightwards double arrow sin space straight theta plus cos space straight theta equals square root of 2 cos space straight theta

straight h right parenthesis space straight L. straight H. straight S. equals open parentheses cosec space straight A minus cot space straight A close parentheses squared
equals open parentheses 1 over sinA minus cosA over sinA close parentheses squared
equals open parentheses fraction numerator 1 minus cosA over denominator sinA end fraction close parentheses squared
equals fraction numerator left parenthesis 1 minus cosA right parenthesis squared over denominator sin squared straight A end fraction
equals fraction numerator left parenthesis 1 minus cosA right parenthesis squared over denominator 1 minus cos squared straight A end fraction
equals fraction numerator left parenthesis 1 minus cosA right parenthesis squared over denominator left parenthesis 1 minus cosA right parenthesis left parenthesis 1 plus cosA right parenthesis end fraction
equals fraction numerator 1 minus cosA over denominator 1 plus cosA end fraction

Hope space this space helps space you.
Please space try space the space next space two space problems space and space get space back space to space us space with space your space solutions. end style

Answered by Rashmi Khot | 15th Jun, 2017, 09:04: AM