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Find the value of the following:

(i) \((\frac{cos47°}{sin43°})^2+(\frac{sin72°}{cos18°})^2-2cos^245°\)

(ii) \(\frac{cos70°}{sin20°}+\frac{cos59°}{sin31°}+{\frac{cosθ}{sin(90°-θ)}}\) - 8cos2 60°

(iii) tan 15° tan 30° tan 45° tan 60° tan 75°

(iv) \(\frac{cot\theta}{tan(90°-\theta)}\) + \(\frac{cos(90°-\theta)tan\theta\,sec(90°-\theta)}{sin(90°-\theta)cot(90°-\theta)cosec(90°-\theta)}\)

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Best answer

(i) \((\frac{cos47°}{sin43°})^2+(\frac{sin72°}{cos18°})^2-2cos^245°\)

(ii) \(\frac{cos70°}{sin20°}+\frac{cos59°}{sin31°}+{\frac{cosθ}{sin(90°-θ)}}\) - 8cos2 60°

(iii) tan 15° tan 30° tan 45° tan 60° tan 75°

(iv) \(\frac{cot\theta}{tan(90°-\theta)}\) + \(\frac{cos(90°-\theta)tan\theta\,sec(90°-\theta)}{sin(90°-\theta)cot(90°-\theta)cosec(90°-\theta)}\)

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