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Trigonometry, 2ADV EQ-Bank 13

Prove the identity \(1+\tan ^2 \theta=\sec ^2 \theta\).   (2 marks)

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\(\text{LHS}\) \(=1+\tan ^2 \theta\)
  \(=1+\dfrac{\sin ^2 \theta}{\cos ^2 \theta}\)
  \(=\dfrac{\cos ^2 \theta+\sin ^2 \theta}{\cos ^2 \theta}\)
  \(=\dfrac{1}{\cos ^2 \theta}\)
  \(=\sec ^2 \theta\)
Show Worked Solution

\(\text{Prove}\ \ 1+\tan ^2 \theta=\sec ^2 \theta\)

\(\text{LHS}\) \(=1+\tan ^2 \theta\)
  \(=1+\dfrac{\sin ^2 \theta}{\cos ^2 \theta}\)
  \(=\dfrac{\cos ^2 \theta+\sin ^2 \theta}{\cos ^2 \theta}\)
  \(=\dfrac{1}{\cos ^2 \theta}\)
  \(=\sec ^2 \theta\)