सिद्ध कीजिए कि :
`2 tan^(-1) [tan(45^(@) - alpha) tan . beta/2] = cos^(-1) ((sin 2 alpha + cos beta)/(1 + sin 2 alpha cos beta))`

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

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

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

Prove that (cos2 alpha-cos 2 beta)/(sin2 alpha+sin2 beta)=tan(beta-alpha)

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

If tan theta = ( tan alpha + tan beta)/(1 + tan alpha tan beta),"show that " sin 2 theta =(sin 2 alpha + sin 2 beta)/(1+sin 2 alpha sin 2 beta)

sin alpha + sin beta= 1/4 and cos alpha + cos beta = 1/3 The vlaue of tan (alpha + beta) is