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.

3 questions · Standard +0.3

1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=1

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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.

Show that \(a ^ { 2 } + b ^ { 2 }\) has a constant value for all values of \(x\).
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}

AQA Paper 2 2024 June Q6

6 marks Standard +0.8

It is given that $$(2 \sin \theta + 3 \cos \theta)^2 + (6 \sin \theta - \cos \theta)^2 = 30$$ and that \(\theta\) is obtuse. Find the exact value of \(\sin \theta\). Fully justify your answer. [6 marks]