Question

Prove that
1 / cos(x) − cos(x) = sin(x) ∙ tan(x) for x ≠ ????2 + k, for all integers k.

Answer 1

Answer: From the given expression we can get the fundamental trigonometry identity

Explanation:

1 ÷ cos (×) - cos (×) = sin (×) * tan (×) ⇒

[1 ÷ cos (×) ] - cos (×) = sin (×)* sin(×)/ cos (×)

1/ cos(×) - cos (×) = sin²(×)/cos(×) ⇒cos(×)/cos(×) -cos²(×) = sin²(×)

1 - cos²(×) = sin²(×)

1= cos²(×) + sin²(×) fundamental trigonometry identity