Question

simplify : (sin A - cos A)²/ sinA^2-cos^2 A​

Answer 1

Answer:

$\dfrac{\sin(A)-\cos(A)}{\sin(A)+(\cos(A)}$

Step-by-step explanation:

We are simplifying the trigonometric expression:

$\dfrac{\left(\dfrac{}{}\sin(A)-\cos(A)\dfrac{}{}\right)^2}{(\sin(A))^2-(\cos(A))^2}$

First, we can expand the denominator using our knowledge of a difference of squares:

• $a^2-b^2=(a+b)(a-b)$

↓↓↓

$\dfrac{\left(\dfrac{}{}\sin(A)-\cos(A)\dfrac{}{}\right)^2}{\left(\dfrac{}{}\sin(A)+(\cos(A)\dfrac{}{}\right)\!\!\left(\dfrac{}{}\sin(A)-(\cos(A)\dfrac{}{}\right)}$

Then, we can cancel the common term $\sin(A)-\cos(A)$ in both the numerator and denominator:

$\boxed{\dfrac{\sin(A)-\cos(A)}{\sin(A)+(\cos(A)}}$