Question

If sinA+cosA=underroot2cos(90-A), then prove that tanA=underroot2+1

Answer 1

Given Equation is

cosA + sinA = \sqrt{2} cos(90 - A )

Using cos(90 - A ) = sinA

cosA + sinA = \sqrt[2] sinA

This can be written as

cosA = \sqrt(2) sinA - sinA

cosA = sinA[ \sqrt(2) - 1 ]

On dividing both side by cosA

cosA/cosA = sinA[ \sqrt(2) - 1 ] /cosA

1 = tanA [ \sqrt(2) - 1 ]

tanA = 1 / [ \sqrt(2) - 1 ]

This can be written as

tanA = [ \sqrt(2) + 1 ] \ [ \sqrt(2) - 1 ] *[ \sqrt(2) + 1 ]

tanA = [ \ sqrt(2) + 1 ] / [ {\sqrt(2) }^2 - 1 ]

tanA = [ \sqrt(2) + 1 ] / [ 2 - 1 ]

tanA = [ \sqrt(2) + 1 ]

Hence Proved