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सिद्ध कीजिए कि tan (pi/3-A) * tan (...

सिद्ध कीजिए कि
` tan (pi/3-A) * tan (pi/3 +A) = ( 2cos 2A+1)/(2 cos 2A-1)`

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Prove that: tan(pi/3-A).tan(pi/3+A)= (2cos2A+1)/(2cos2A-1)

Prove that: tan(pi/3-A).tan(pi/3+A)= (2cos2A+1)/(2cos2A-1)

prove that tan ((pi) / (4) + (1) / (2) cos ^ (- 1) ((a) / (b))) + tan ((pi) / (4) - (1) / (2) cos ^ (- 1) ((a) / (b))) = (b) / (a) cos ^ (- 1) ((cos x + cos y) / (1 + cos x cos y) ) = 2tan ^ (- 1) ((tan x) / (2) (tan y) / (2))

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sin ^(2)(pi/6) + cos ^(2)(pi/3) - tan ^(2)(pi/4) =- 1/2

If x != 0 , then tan((pi)/4 + 1/2 cos^(-1) x) + tan ((pi)/4 - 1/2 cos^(-1) x) = ......

Statement I y = tan^(-1) ( tan x) " and " y = cos^(-1) ( cos x) " does not have nay solution , if " x in (pi/2, (3pi)/2) Statement II y = tan^(-1)( tan x) = x - pi, x in (pi/2, (3pi)/2) " and " y = cos^(-1) ( cos x) = {{:(2pi - x", " x in [pi, (3pi)/2]),(" x, " x in [pi/2,pi]):}

Statement I y = tan^(-1) ( tan x) " and " y = cos^(-1) ( cos x) " does not have nay solution , if " x in (pi/2, (3pi)/2) Statement II y = tan^(-1)( tan x) = x - pi, x in (pi/2, (3pi)/2) " and " y = cos^(-1) ( cos x) = {{:(2pi - x", " x in [pi, (3pi)/2]),(" x, " x in [pi/2,pi]):}