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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)

Grade:11

1 Answers

Vikas TU
14149 Points
4 years ago
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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