Chapter 8: Q. 26 (page 516)

Find the exact value of the expression-
$c o t 40 ° - \frac{\sin 50 °}{\sin 40 °}$

Short Answer

Expert verified

The required value is,

$c o t 40 ° - \frac{\sin 50 °}{\sin 40 °} = 0$

Step by step solution

Step 1. Given information

Given expression,

$c o t 40 ° - \frac{\sin 50 °}{\sin 40 °}$

Step 2. Calculation

Solving the given expression,

$c o t 40 ° - \frac{\sin 50 °}{\sin 40 °} = \frac{\cos 40 °}{\sin 40 °} - \frac{\sin 50 °}{\sin 40 °}$ --------- $(c o t θ = \frac{\cos θ}{\sin θ})$

$= \frac{\cos 40 ° - \sin 50 °}{\sin 40 °} = \frac{\cos (90 ° - 50 °) - \sin 50 °}{\sin 40 °} = \frac{\sin 50 ° - \sin 50 °}{\sin 40 °} = 0$ ---------- $\{\cos (90 ° - θ) = \sin θ\}$

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Find the exact value of the expression-
$c o t 40 ° - \frac{\sin 50 °}{\sin 40 °}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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Find the exact value of the expression-cot40°-sin50°sin40°

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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Find the exact value of the expression-
$c o t 40 ° - \frac{\sin 50 °}{\sin 40 °}$