Question

Cos inverse x square -1/x square +1+1/2 tan inverse -2x /1-xsquare

Answer 1

Answer:

Step-by-step explanation:

tan^-1{(1/√3)tan(x/2)}

=(1/2) 2tan^-1{(1/√3)tan(x/2)}

=(1/2)cos^-1[{(1-(1/3)tan²(x/2)}/{(1+(1/3)tan²(x/2)}]

=(1/2)cos^-1[{3-tan²(x/2)}/{3+tan²(x/2)}]

=(1/2)cos^-1[{3-(1-cosx)/(1+cosx)}/{3+(1-cosx)/(1+cosx)}]

=(1/2)cos^-1{(2+4cosx)/(4+2cosx)}

=(1/2)cos^-1{(1+2cosx)/(2+cosx)}(Proved)

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