If `(ntan theta)/(cos^(2)(alpha-theta))=(m tan(alpha-theta))/(cos^(2)theta)`, then show that,
`2 theta=alpha-tan^(-1)((n-m)/(n+m)tan alpha)`

"If" (n tan theta)/(cos^(2) (alpha - theta))= (m tan (alpha - theta))/(cos^(2) theta) "then show that" tan ( alpha - 2 theta) = (n-m)/(n+m) tan alpha

If phi=cot^(-1)sqrt(cos2theta)-tan^(-1)sqrt(cos2theta) , then show that, sin phi=tan^(2)theta .

If tan theta = sec 2 alpha, "show that", sin 2 theta = (1-tan^(4) alpha)/(1+ tan^(4) alpha).

If cos^(3) theta = kcos (alpha- 3 theta) and sin ^(3) theta= ksin (alpha-3 theta) , then show that 2k^(2)-k cos alpha-1=0

If tan theta = ( tan alpha - tan beta)/(1-tan alpha tan beta),"show that", sin 2 theta=(sin 2 alpha- sin 2 beta)/(1- sin2 alpha sin 2 beta).

If tan beta = (n sin alpha cos alpha)/(1-n sin^(2) alpha), "show that", tan (alpha - beta) = (1 - n) tan alpha.

If cos^2alpha=sin^3alpha then show that tan^6alpha-tan^2alpha=1

If cos^3theta=kcos(alpha-3theta) and sin^3theta=k sin(alpha-3theta) ,show that 2k^2-kcosalpha-1=0

Show that (1)/(3) lt (sec^(2) theta - tan theta)/( sec^(2) theta+ tan theta) lt3 .

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)