If 0 π/2, show that (tan x+sin x) 1/2 + (tan x- sin x) 1/2 =2(tan x) 1/2 cos( π/4-x/2)

Question

If 0 π/2, show that (tan x+sin x) 1/2 + (tan x- sin x) 1/2 =2(tan x) 1/2 cos( π/4-x/2)

Vikas TU · Answer

Taking L.H.S (tan x+sin x) 1/2 + (tan x- sin x) ½ Write tanx = sinx/cosx and then take L.CM. for all final eqn. will become, root(sinx/cosx)*root(1+cosx/1-cosx) => root(tanx)*(1 +cosx)/sinx Now apply the formulae sor sin2x and cos2x just for in the form sinx and cosx x will be in x/2. thus. now u can do further.

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If 0 π/2, show that (tan x+sin x) 1/2 + (tan x- sin x) 1/2 =2(tan x) 1/2 cos( π/4-x/2)

If 0 π/2, show that (tan x+sin x)^1/2 + (tan x- sin x)^1/2=2(tan x)^1/2 cos( π/4-x/2)

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If 0 π/2, show that (tan x+sin x) 1/2 + (tan x- sin x) 1/2 =2(tan x) 1/2 cos( π/4-x/2)

If 0 π/2, show that (tan x+sin x)1/2 + (tan x- sin x)1/2=2(tan x)1/2 cos( π/4-x/2)

1 Answers

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If 0 π/2, show that (tan x+sin x)^1/2 + (tan x- sin x)^1/2=2(tan x)^1/2 cos( π/4-x/2)