Question

Prove the following

Answer 1

Explanation:

Sin² x - Cos² x = (1 - Cos² x ) - Cos² x {Sin² x + Cos² x = 1}

= 1 - 2Cos² x

= - (2Cos x -1)

`= -((2)/(Sec^(2) x) - 1)\\\\=-(( 2)/(Sec^(2) \ x)-(Sec^(2) \ x)/(Sec^(2) \ x))\\\\=-((2-Sec^(2) \ x)/(Sec^(2) \ x))\\\\=(2-Sec^(2) \ x )/(-Sec^(2) \ x)`

Hence proved