Nikit0123V
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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​

Respuesta :

CHERLYNnotCHERRY

Answer:

The steps are :

[tex] {tan}^{2} θ - {cot}^{2} θ = {sec}^{2} θ(1 - {cot}^{2} θ)[/tex]

[tex]RHS = {sec}^{2} θ(1 - {cot}^{2} θ)[/tex]

[tex]RHS = (1 + {tan}^{2} θ)(1 - \frac{1}{ {tan}^{2} θ} )[/tex]

[tex]RHS = (1 + {tan}^{2} θ)( \frac{ {tan}^{2}θ - 1}{ {tan}^{2} θ} )[/tex]

[tex]RHS = - \frac{(1 + {tan}^{2}θ)(1 - {tan}^{2} θ)}{ {tan}^{2} θ}[/tex]

[tex]RHS = - \frac{(1 - {tan}^{4} θ)}{ {tan}^{2} θ} [/tex]

[tex]RHS = \frac{ {tan}^{4} θ - 1}{ {tan}^{2}θ } [/tex]

[tex]RHS = {tan}^{2} θ - \frac{1}{ {tan}^{2}θ } [/tex]

[tex]RHS = {tan}^{2} θ - {cot}^{2} θ[/tex]

[tex]RHS = LHS (proven)[/tex]

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