2.(a) Express √2 cos x - √5 sin x in the form R cos(x + α), where R > 0 and 0° < α < 90°. Give the exact value of R and the value of a correct to 3 decimal places.
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(b) Hence solve the equation √2 cos 2θ - √5 sin 2θ = 1, for 0° < θ < 180°.
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Prove the converse of the pythagorean theorem using similar triangles. the converse of the pythagorean theorem states that when the sum of the squares of the lengths of the legs of the triangle equals the squares length of the hypotenuse, the triangle is a right triangle. be sure to create and name the appropriate geometric figures.