Question

Sin A + cos A/ sin A - cos A +sin A - cos A /sin A + cos A​

Answer 1

$\\ \sf\longmapsto \dfrac{sinA+cosA}{sinA-cosA}+\dfrac{sinA-cosA}{sinA+cosA}$

Let

• sinA be a
• cosA be b

$\\ \sf\longmapsto \dfrac{a+b}{a-b}+\dfrac{a-b}{a+b}$

$\\ \sf\longmapsto \dfrac{(a+b)^2+(a-b)^2}{(a+b)(a-b)}$

$\\ \sf\longmapsto \dfrac{2(a^2+b^2)}{a^2-b^2}$

• Putting values

$\\ \sf\longmapsto \dfrac{2(sin^2A+cos^2A)}{sin^2A-cos^2A}$

$\\ \sf\longmapsto \dfrac{2}{sin^2A-cos^2A}$