Question

is this identity always true?
how​

Answer 1

yeah this identity is always universally true

Answer 2

Step-by-step explanation:

Cosec² theta - cot² theta = 1

we know, cosec² theta = 1/sin²theta  && cot² theta = cos² theta/sin² theta

Substituting this:

1/sin² theta - cos² theta/sin² theta

= [1-cos² theta]/sin² theta

Again we know cos² theta + sin² theta = 1, so 1-cos²theta = sin²theta

= sin²theta/sin²theta = 1 = RHS. Hence proved forever

Additional info:

Why sin²theta + cos²theta = 1

From trig ratio:

sin theta = opposite side/Hypotenuse

cos theta = Adjacent side/hypotenuse

sin² theta + cos² theta = opposite side²/hypotenuse² + adjacentside²/hypot²

                     = [opposite side²+ adjacent side²]/hypotenuse²

From Pythagoras theorem: base²+height² = hypotenuse²

Here base and height are adjacent and opposite sides

        = hypotenuse²/hypotenuse² = 1