[" Show that "],[qquad 2+an^(-1){tan(a)/(2)*tan((pi)/(4)-(3)/(2))=tan^(-1)(sin alpha^(2)cos beta)/(cos^(2)+sin pi)]

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))

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))

" 1.Prove that : "sin^(2)(pi)/(6)+cos^(2)(pi)/(3)-tan^(2)(pi)/(4)=-(1)/(2)

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

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

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