Question

sin(90-A)/1-tanA + cos(90-A)/1-cosA = cosA + sinA​

Answer 1

Step-by-step explanation:

sin(90-A)/1-tanA+cos(90-A)/1-cotA

=cosA/1-tanA+sinA/1-cotA

=cos²A/cosA-sinA+sin²A/sinA-cosA

=(cos²A/cosA-sinA)-(sin²A/cosA-sinA)

=(cos²A-sin²A/cosA-sinA)

=cosA+sinA

Answer 2

$\Large\boxed{\mathcal\red{Correct \ Question}}$

sin(90°-A)/1-tanA +cos(90-A)/1-cotA = cosA + sinA

$\huge\boxed{\mathcal\green{SoLution}}$

→ Solving L.H.S

sin(90-A)/1-tanA+cos(90-A)/1-cotA

=cosA/1-tanA+sinA/1-cotA

=cos²A/cosA-sinA+sin²A/sinA-cosA

=(cos²A/cosA-sinA)-(sin²A/cosA-sinA)

=(cos²A-sin²A)/(cosA-sinA)

=cosA+sinA