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Question

Given : $$sec\, A\, =\, \displaystyle \frac{29}{21}$$, evaluate : $$sin\, A\, -\, \displaystyle \frac{1}{tan\, A}$$ is $$\displaystyle -\frac{m}{580}$$, m is 


A
130
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B
215
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C
209
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D
524
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Solution

The correct option is C 209
$$\sec A = \frac{29}{21}$$
$$\sec A = \frac{H}{B} = \frac{29}{21}$$
Using Pythagoras Theorem,
$$H^2 = P^2 + B^2$$
$$29^2 = P^2 + 21^2$$
$$841 = 441 + P^2$$$
$$P = 20$$
Now, $$\sin A - \frac{1}{\tan A} = \sin A - \cot A$$
= $$\frac{P}{H} - \frac{B}{P}$$
= $$\frac{20}{29} - \frac{21}{20}$$
= $$\frac{400 - 609}{580}$$
= $$\frac{- 209}{580}$$

Mathematics

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