" Q.23prove that "2tan^(-1)(tan(alpha)/(2)tan((pi)/(4)-(beta)/(2)))=tan^(-1)((sin alpha cos beta)/(sin beta+cos alpha))

Prove that 2tan^(-1)[tan((alpha)/(2)) tan((pi)/(4)-(beta)/(2))]=tan^(-1)((sin alpha cos beta)/(cos alpha+sin beta))

Show taht 2tan ^ (- 1) (tan ((alpha) / (2)) tan ((pi) / (4) - (beta) / (2))) = tan ^ (- 1) ((sin alpha cos beta) / (cos alpha + sin beta))

(sin^(2)alpha-sin^(2)beta)/(sin alpha cos alpha-sin beta cos beta)=tan(alpha+beta)

if 3tan alpha=4tan beta then prove that tan(alpha-beta)=(tan beta)/(4tan^(2)beta+3)=(sin beta*cos beta)/(3+sin^(2)beta)

Prove that: tan(alpha+beta)tan(alpha-beta)=(sin^2 alpha-sin^2 beta)/(cos^2 alpha-sin^2 beta)

Prove that: tan^(-1){(cos2 alpha sec2 beta+cos2 beta sec2 alpha)/(2)}=tan^(-1){tan^(2)(alpha+beta)tan^(2)(alpha-beta)}+tan

If tan(alpha-beta)=(sin2 beta)/(3-cos2 beta), then ( i )tan(alpha)=2tan(beta)( ii) (1)/(2)tan(alpha)=tan(beta)( (ii) 2tan(alpha)=3tan(beta)( iv) 3tan(alpha)=2tan(beta)

If cos theta=(cos alpha cos beta)/(1-sin alpha sin beta), prove that one value of (tan)(theta)/(2)=((tan alpha)/(2)-(tan beta)/(2))/(1-tan(alpha)/(2)(tan beta)/(2))