Prove using Pythagorean identity result

A question is this type if and only if it asks to show a relationship between sin x and cos x given as constants (like sin x = a + b, cos x = a - b) using the Pythagorean identity.

2 questions · Standard +0.0

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CAIE P1 2019 June Q4
5 marks Moderate -0.3
4 Angle \(x\) is such that \(\sin x = a + b\) and \(\cos x = a - b\), where \(a\) and \(b\) are constants.
  1. Show that \(a ^ { 2 } + b ^ { 2 }\) has a constant value for all values of \(x\).
  2. In the case where \(\tan x = 2\), express \(a\) in terms of \(b\).
OCR MEI AS Paper 2 Specimen Q12
3 marks Standard +0.3
12 Given that \(\arcsin x = \arccos y\), prove that \(x ^ { 2 } + y ^ { 2 } = 1\). [Hint: Let \(\arcsin x = \theta\) ] \section*{END OF QUESTION PAPER}