if sinA +cosA =√3, then prove that tanA +cotA =1

Asked by singh.dh | 12th Jan, 2020, 10:42: PM

Expert Answer:

Given: sinA +cosA =√3
We need to prove that tanA +cotA =1
sin A plus cos A equals square root of 3
rightwards double arrow sin squared A plus cos squared A plus 2 sin A cos A equals 3
rightwards double arrow 1 plus 2 sin A cos A equals 3
rightwards double arrow 2 sin A cos A equals 2
rightwards double arrow sin A cos A equals 1
C o n s i d e r comma
tan A plus c o t A
equals fraction numerator sin A over denominator cos A end fraction plus fraction numerator cos A over denominator sin A end fraction
equals fraction numerator sin squared A plus cos squared A over denominator sin A cos A end fraction
equals fraction numerator 1 over denominator sin A cos A end fraction equals 1

Answered by Renu Varma | 13th Jan, 2020, 10:34: AM