Question

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

plzz help me...tomorrow there is opt math test in my school...If I fail then i have to leave opt classes and go to eco....our teacher only taught trigonometry and I was absent 2 3 days due to sickness...plzz help me​

Answer 1

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)`