If sin A+cos A=√2 sin(90-A),show that cot A=√2+1

Asked by Sunita | 31st Mar, 2018, 07:53: PM

Expert Answer:

begin mathsize 16px style sin space straight A plus cos space straight A equals square root of 2 space sin space left parenthesis 90 minus straight A right parenthesis
rightwards double arrow sin space straight A plus cos space straight A equals square root of 2 space cos space straight A
rightwards double arrow sin space straight A equals square root of 2 space cos space straight A minus cos space straight A
rightwards double arrow sin space straight A equals cos space straight A left parenthesis square root of 2 minus 1 right parenthesis
rightwards double arrow 1 equals fraction numerator cos space straight A over denominator sin space straight A end fraction square root of 2 minus 1
rightwards double arrow cot space straight A equals fraction numerator 1 over denominator square root of 2 minus 1 end fraction
rightwards double arrow cot space straight A equals fraction numerator 1 over denominator square root of 2 minus 1 end fraction cross times fraction numerator square root of 2 plus 1 over denominator square root of 2 plus 1 end fraction
rightwards double arrow cot space straight A equals fraction numerator square root of 2 plus 1 over denominator 2 minus 1 end fraction
rightwards double arrow cot space straight A equals square root of 2 plus 1 end style

Answered by Rashmi Khot | 31st Mar, 2018, 08:51: PM