Show that `((1+tan ^(2) A) /(1+cot ^(2) A ) ) =((1- tanA )/( 1-cot A ))^(2)= tan ^(2) A `

Show that (1- tan ^(2) A ) /( cot ^(2) A-1) =tan ^(2) A

Prove the following identities. where the angles involved are acute angles for which the expressions are defined. ((1+tan^(2)A)/(1+cot^(2)A))=((1-tanA)/(1-cotA))^(2)=tan^(2)A

Show that ( tan^(-1) 1 + tan^(-1) 2 + tan^(-1) 3) = pi

( 1-tan ^(2) 45^(@) )/( 1+tan ^(2) 45^(@)) =

int(1+tan^(2)x)/(1-tan^(2)x)dx=....

Prove the following identities : (1+tan^(2)theta)/(1+cot^(2)theta)=((1-tantheta)/(1-cottheta))^(2)

(d)/(dx ) (tan^(-1)x + cot^(-1) x) = ……

Prove that sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3)=15

By using above basic addition/ subtraction formulae, prove that (i) tan (A+B)=(tan A+tan B)/(1-tan A tan B) , (ii) tan (A-B)=(tan A-tanB)/(1+tan A tan B) (iii) sin2theta=2sintheta costheta , (iv) cos2theta=cos^(2)theta=1-2sin^(2)theta=2cos^(2)theta-1 (v) tan 2theta=(2 tan theta)/(1-tan^(2) theta)

Prove that tan 70^(@)=cot70^(@)+2cot40^(@)