If sin-45- what is the value of -cosec- -

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Complementary Trigonometric Ratios

If sinθ=45, w...

Question

If $\sin θ = \frac{4}{5}$ , what is the value of cotθ + cosecθ?

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Solution

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s i n θ \times c o s e c θ \times c o t θ

sin Θ + cosec Θ = 2

cot Θ + cos Θ

cotθ = \frac{40}{9}

\frac{1}{c o s e c θ + cot θ} - \frac{1}{sin θ} = \frac{1}{sin θ} - \frac{1}{c o s e c θ - cot θ}

\frac{1}{cosec θ + cot θ} - \frac{1}{sin θ} = \frac{1}{sin θ} - \frac{1}{cosec θ - cot θ}

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