Come si dimostra $(1-sin ^ 2theta) (1 + cot ^ 2theta) = cot ^ 2theta$ ?

Vedi sotto.

Lo sappiamo ,

$(1)cos^2x+sin^2x=1$
$(2)csc^2x-cot^2x=1$
$(3)cscx=1/sinx$
$(4)cosx/sinx=cotx$

utilizzando $(1) and (2):$

$LHS=(1-sin^2theta)(1+cot^2theta)$

$LHS=cos^2thetacsc^2thetatoApply(3)$

$LHS=cos^2theta*1/sin^2theta$

$LHS=cos^2theta/sin^2thetatoApply(4)$

$LHS=cot^2theta$

$LHS=RHS$

Come si dimostra (1-sin ^ 2theta) (1 + cot ^ 2theta) = cot ^ 2theta (1-sin ^ 2theta) (1 + cot ^ 2theta) = cot ^ 2theta ?