Prove Pythagorean identity from triangle

A question is this type if and only if it asks to prove sin²θ + cos²θ = 1 or a related identity (like 1 + tan²x = sec²x) using a right-angled triangle diagram.

3 questions · Easy -1.2

Sort by: Default | Easiest first | Hardest first
OCR MEI C2 Q7
5 marks Easy -1.2
7
  1. Using the triangle, show that \(\sin ^ { 2 } x + \cos ^ { 2 } x = 1\).
  2. Hence prove that
    \includegraphics[max width=\textwidth, alt={}]{73d1c02b-1b7b-426d-a171-c762597cfed4-2_255_501_1779_1022} \(1 + \tan ^ { 2 } x = \frac { 1 } { \cos ^ { 2 } x }\).
OCR MEI C3 Q5
3 marks Easy -1.2
5 Use the triangle in Fig. 4 to prove that \(\sin ^ { 2 } \theta + \cos ^ { 2 } \theta = 1\). For what values of \(\theta\) is this proof valid? \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{64cb5e15-35b0-43a3-9f6d-f8e1c04b80b8-1_357_595_1831_798} \captionsetup{labelformat=empty} \caption{Fig. 4}
\end{figure}
OCR MEI C3 2011 January Q4
3 marks Easy -1.2
4 Use the triangle in Fig. 4 to prove that \(\sin ^ { 2 } \theta + \cos ^ { 2 } \theta = 1\). For what values of \(\theta\) is this proof valid? \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{9857ad89-b315-4cd6-8d8d-26a509ca52a8-2_362_606_906_772} \captionsetup{labelformat=empty} \caption{Fig. 4}
\end{figure}