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Here , firstlywe have to assume
cot^-1 (√cosx) = A , => cotA = √cosx
tan^-1 ( √cosx ) = B => tanB = √cosx
then find sinA,cosA , sinB and cosB
now, use formula ,
sin(A - B) = sinA.cosB - cosA.sinB
then put
finally use formula,
(1 - cosx) = 2sin²(x/2)
(1 + cosx) = 2cos²(x/2)