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.

2 questions · Easy -1.2

1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=1
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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
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? [3] \includegraphics{figure_4}