Question

(1 + tan’0) (1 - cos²0) = tan²0​

Answer 1

You have to apply Trigonometry Formula :

`{sin}^(2) θ + {cos}^(2) θ = 1`

`1 + {tan}^(2) θ = {sec}^(2) θ`

Next, you have to prove it :

`(1 + {tan}^(2) θ)(1 - {cos}^(2) θ) = {tan}^(2) θ`

`LHS = (1 + {tan}^(2) θ)(1 - {cos}^(2) θ)`

`LHS = ( {sec}^(2) θ)( {sin}^(2) θ)`

`LHS = ( \frac{1}{ {cos}^(2) θ} )( {sin}^(2) θ)`

`LHS = \frac{ {sin}^(2) θ}{ {cos}^(2) θ}`

`LHS = {tan}^(2) θ`

`∴LHS = RHS \: (proven)`