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Trigonometric Equations

Equations with trigonometry in them can look scary, but that's nothing that a quick little substitution can't fix.

Level 2

         

Find all values of \( \theta \) such that

\[ \cos^2 \theta = 1. \]

In the options, \(n\) is an integer.

Given that

\[ \cos(A)-4\sin(A)=1,\]

what are the possible values of

\[ \sin(A) + 4\cos(A)? \]

\[\large\sin\theta+\cos\theta=\sqrt{2}\sin(90^{\circ}-\theta), \ \ \ \ \ \cot\theta = \ ? \]

Give your answer to 3 decimal places.

Find the value of \(x\) between 0 and 180 such that

\[\tan({ 120 }^{ \circ }-x^{ \circ })=\frac { \sin{ 120 }^{ \circ }-\sin x^{ \circ } }{ \cos{ 120 }^{ \circ }-\cos x^{ \circ }}.\]

If \[\quad \quad \dfrac{\cos^4\alpha}{\cos^2\beta}+\dfrac{\sin^4\alpha}{\sin^2\beta}=1,\] find the value of \[\dfrac{\sin^4\beta}{\sin^2\alpha}+\dfrac{\cos^4\beta}{\cos^2\alpha}.\]

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