Question

if m=tan theta+ain't theta and n=tan theta-sin theta then m square-n square

Answer 1

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⭐⭐⭐⭐⭐ ANSWER ⭐⭐⭐⭐⭐
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Given, m = tan theta + sin theta

n = tan theta - sin theta


Now here, I am holding "THETAS" as "x".

So, mn = (tan x + sin x) (tan x - sin x)

=> mn = tan²x - sin²x

=> mn = (sin²x/cos²x) - sin²x

=> mn = sin²x (1/cos²x - 1)

=> mn = sin²x (1-cos²x/cos²x)

=> mn = sin²x (sin²x/cos²x)

=> mn = sin²x tan²x

=> mn = (sin x tan x)²

=> √mn = sin x tan x


Therefore, m²-n²

= (tan x + sin x)² - (tan x - sin x)²

= tan²x + 2 sin x tan x + sin² x - tan²x + 2 tan x sin x - sin² x

= 2 sin x tan x + 2 sin x tan x

= 4 sin x tan x

= 4 √mn [REQUIRED ANSWER]



THUS, THE QUESTION GETS SOLVED (^_^)


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⭐⭐⭐ ALWAYS BE BRAINLY ⭐⭐⭐

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