Question

7. Prove that: sin A + cos A/sin A -cos A+sin A- cosA/ sin A + cos A= 2/1-2 cos^2-A​

Answer 1

Step-by-step explanation:

$\frac{sinA+cosA}{sinA-cosA} + \frac{sinA-cosA}{sinA+cosA} \\ = \frac{(sinA+cosA)²+(sinA-cosA)²}{(sinA-cosA)(sinA+cosA)} \\ = \frac{sin²A+2sinAcosA+cos²A+sin²A-2sinAcosA+cos²A}{Sin²A-cos²A} \\ = \frac{2}{1-Cos²A-cos²A} \\ = \frac{2}{1-2cos²A}$