Question

C) tan^2A - cot^2A = sec^2A (1 - cot^2A)

Answer 1

Answer:

The steps are :

${tan}^{2} θ - {cot}^{2} θ = {sec}^{2} θ(1 - {cot}^{2} θ)$

$RHS = {sec}^{2} θ(1 - {cot}^{2} θ)$

$RHS = (1 + {tan}^{2} θ)(1 - \frac{1}{ {tan}^{2} θ} )$

$RHS = (1 + {tan}^{2} θ)( \frac{ {tan}^{2}θ - 1}{ {tan}^{2} θ} )$

$RHS = - \frac{(1 + {tan}^{2}θ)(1 - {tan}^{2} θ)}{ {tan}^{2} θ}$

$RHS = - \frac{(1 - {tan}^{4} θ)}{ {tan}^{2} θ}$

$RHS = \frac{ {tan}^{4} θ - 1}{ {tan}^{2}θ }$

$RHS = {tan}^{2} θ - \frac{1}{ {tan}^{2}θ }$

$RHS = {tan}^{2} θ - {cot}^{2} θ$

$RHS = LHS (proven)$