Question

cot^2 A- cot^2B=cos^2A-cos^2B/sin^2A × sin^2B=cosec^2 A-cosec^B​

Answer 1

Step-by-step explanation:

$\bf\huge \mathfrak{Question}$

$\bf \: cot^2 A - cot^2B = cos^2A - \frac{cos^2B}{sin^2A} × sin^2B = cosec^2A - cosec^B$

$\bf\huge \mathfrak{solution}$

$\bf \:cot^2A - cot^2B =cos^2A/sin^2A - cos^2B/sin^2B$

$\bf \:=>(cos^2Asin^2B - sin^2Acos^2B)/sin^2ASin^2B$

$\bf \: =>(cos^2A-cos^2Acos^2B-cos^2B +cos^2Acos^2B)/sin^2Asin^2B$

$\bf \:=> (cos^2A-cos^2B)/sin^2Asin^2B$

$\bf\huge \mathfrak{PROVED}$