Question

cosA-sinA=1 prove that cosA+sinA=+_1

Answer 1

sinA1+cosAsin⁡A1+cos⁡A

=(sinA)(1−cosA)1−cos2A=(sin⁡A)(1−cos⁡A)1−cos2⁡A

=(sinA)(1−cosA)sin2A=(sin⁡A)(1−cos⁡A)sin2⁡A

=1−cosAsinA=1−cos⁡Asin⁡A

=1sinA−cosAsinA=1sin⁡A−cos⁡Asin⁡A

=cosecA−cotA=cosecA−cot⁡A

∴sinA1+cosA=cosecA−cotA

Answer 2

sinA1+cosAsin⁡A1+cos⁡A

=(sinA)(1−cosA)1−cos2A=(sin⁡A)(1−cos⁡A)1−cos2⁡A

=(sinA)(1−cosA)sin2A=(sin⁡A)(1−cos⁡A)sin2⁡A

=1−cosAsinA=1−cos⁡Asin⁡A

=1sinA−cosAsinA=1sin⁡A−cos⁡Asin⁡A

=cosecA−cotA=cosecA−cot⁡A

∴sinA1+cosA=cosecA−cotA