SATHEE: Trigonometrical Ratios and Identities 1 Question 13

Trigonometrical Ratios and Identities 1 Question 13

13. The value of the expression $\sqrt{3} cosec 20^{\circ} - \sec 20^{\circ}$ is equal to

$(1988, 2 M)$

(a) 2

(b) $2 \sin 20^{\circ} \sin 40^{\circ}$

(d) $Extra open brace or missing close brace$

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Answer:

Correct Answer: 13. (b)

Solution:

Given expression $=$

$\sqrt{3} cosec 20^{\circ} - \sec 20^{\circ} = \tan 60^{\circ} cosec 20^{\circ} - \sec 20^{\circ}$

$\begin{aligned} = \frac{\sin 60^{\circ} \cos 20^{\circ} - \cos 60^{\circ} \cdot \sin 20^{\circ}}{\cos 60^{\circ} \cdot \sin 20^{\circ} \cdot \cos 20^{\circ}} \\ = \frac{\sin (60^{\circ} - 20^{\circ})}{\cos 60^{\circ} \cdot \sin 20^{\circ} \cdot \cos 20^{\circ}} = \frac{\sin 40^{\circ}}{\frac{1}{2} \cdot \sin 20^{\circ} \cos 20^{\circ}} \\ = \frac{2 \sin 20^{\circ} \cos 20^{\circ}}{\frac{1}{2} \sin 20^{\circ} \cos 20^{\circ}} = 4 \end{aligned}$

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Trigonometrical Ratios and Identities 1 Question 13

13. The value of the expression 3cosec20∘−sec⁡20∘ is equal to

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13. The value of the expression $\sqrt{3} cosec 20^{\circ} - \sec 20^{\circ}$ is equal to