Question

sin x - sin 3 x / sin ² x - cos ² x = 2 sin x​

Answer 1

Step-by-step explanation:

cos²x can be written as sin²x+1 because the identity is sin²x + cos ² x =1

Answer 2

Step-by-step explanation:

  $\frac{sinx-sin3x}{sin^{2}x -cos^{2} x } = 2sinx$

⇒$LHS$

⇒$\frac{sinx - (3sinx - 4sin^{3}x)}{sin^{2}x -cos^{2}x }$         --------- $sin3x = 3sinx - 4sin^{3}x$

⇒$\frac{-2sinx+4sin^{3}x }{sin^{2}x -cos^{2}x }$                

⇒$\frac{-2sinx(1 - 2sin^{2}x) }{-cos2x}$              --------- $taking$ $-2sinx$ $common$

⇒$2sinx$                              --------- $1 - 2sin^{2}x = cos2x$