Question

If cot theta + cos theta = X and cot theta - cos theta = Y then xsquare - ysquare is

Answer 1

$\bf\large\underline\red{Answer:-}$

➜ 0

Given :-

➜ CotQ + CosQ = X

➜ CotQ - CosQ = Y

➤ To find :- x2 - y2 =?

$\bf\large\underline\blue{Step by Step Explanation :-}$

➜ x2 - y2

➜ (CotQ + CosQ)2 - (CotQ - CosQ)2

$\bf\small\underline{Identity :-}$

➜ (a+b)2 = a2 + b2 - 2ab

➜ (a-b)2 = a2 + b2 - 2ab

So,

➜ Cot2Q + Cos2Q + 2 CotQ CosQ - ( Cot2Q + Cos2Q - 2CotQ CosQ)

➤So, now we will open the bracket,

➜ Cot2Q + Cos2Q + 2CotQ CosQ - Cot2Q - Cos2Q + 2CotQ CosQ

➜ 0

➤ Therefore x2 - y2 = 0

Hope it will help you !