question

Asked by arindeep.singh | 10th Sep, 2020, 07:04: PM

Expert Answer:

Given: sec theta + tan theta = p
TO find: sin theta
Let space secθ space plus thin space tanθ space equals space straight p space... space left parenthesis straight i right parenthesis
sec squared straight theta minus tan squared straight theta equals 1
rightwards double arrow open parentheses secθ plus tanθ space close parentheses open parentheses secθ minus tanθ space close parentheses equals 1
rightwards double arrow secθ minus tanθ equals 1 over straight p... left parenthesis ii right parenthesis
Adding space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma space we space get
secθ equals fraction numerator straight p squared plus 1 over denominator 2 straight p end fraction rightwards double arrow cosθ equals fraction numerator 2 straight p over denominator 1 plus straight p squared end fraction
rightwards double arrow sinθ equals square root of 1 minus cos squared straight theta end root equals square root of 1 minus fraction numerator 2 straight p over denominator open parentheses 1 plus straight p squared close parentheses squared end fraction end root equals fraction numerator 1 minus straight p squared over denominator 1 plus straight p squared end fraction

Answered by Renu Varma | 10th Sep, 2020, 07:48: PM