SOLUTION: solve tan x + sin x = m and tan x –sin x = n, then (m 2 – n 2 ) is equal

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Question 902930: solve tan x + sin x = m and tan x –sin x = n, then (m 2 – n 2 ) is equal
Answer by mananth(16946) About Me  (Show Source):
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tan x + sin x = m and tan x –sin x = n, then (m 2 – n 2 ) is equal
m^2= (tan x+sin x)^2
n^2= (tan x-sin x)^2
m^2-n^2= (tan x+sin x)^2 -(tan x-sin x)^2
= tan^2x+2tanxsinx+sin^2x-(tan^2x-2tanx.sinx+sin^2x)
= tan^2x+2tanxsinx+sin^2x-tan^2x+2tanx.sinx-sin^2x
= 4 tanx sinx