Question

11 sin70°/ 7 cos20° - 4/7 cos53° cosec 37° / tan 15° tan 35° tan 55° tan 75° ​

Answer 1

Answer:

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Answer 2

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To Solve:

• $\dfrac{11\sin 70^{\circ}}{4\cos 20^{\circ}} - \dfrac{4}{7} \dfrac{\cos 53^{\circ} \csc 37^{\circ}}{\tan 15^{\circ} \tan 35^{\circ} \tan 55^{\circ} \tan 75^{\circ}}$

Solution:

$\dfrac{11\sin 70^{\circ}}{4\cos 20^{\circ}} - \dfrac{4}{7} \dfrac{\cos 53^{\circ} * \csc 37^{\circ}}{\tan 15^{\circ} * \tan 35^{\circ} * \tan 55^{\circ} * \tan 75^{\circ}}\\\\\implies \dfrac{11\sin 70^{\circ}}{4\cos (90-70)^{\circ}} - \dfrac{4}{7} \dfrac{\cos 53^{\circ} * \csc (90-53)^{\circ}}{\tan 15^{\circ} * \tan 35^{\circ} * \tan (90-35)^{\circ} * \tan (90-15)^{\circ}}\\\\\implies \dfrac{11\sin 70^{\circ}\!\!\!\!\!\!\!\!\!\!\!\!\!\huge{/}\:}{4\sin 70^{\circ}\!\!\!\!\!\!\!\!\!\!\!\!\!\huge{/}\:} - \dfrac{4}{7} \dfrac{\cos 53^{\circ} \!\!\!\!\!\!\!\!\!\!{\huge{/}}\:\:\:\:\: * \dfrac{1}{\cos 53^{\circ}}\!\!\!\!\!\!\!\!\!\!\!\huge{/}}{(\tan 15^{\circ}\!\!\!\!\!\!\!\!\!\!\!/ \:\:\:\:\:\:\: * \cot 15^{\circ}\!\!\!\!\!\!\!\!\!\!{/} \:\:\:\:\:\: * )(\cot 35^{\circ}\!\!\!\!\!\!\!\!\!\!\!\!{/} \:\:\:\:\:\:\:\: * \tan 35^{\circ}\!\!\!\!\!\!\!\!\!\!{/})}\\\\\implies \dfrac{11}{7} - \dfrac{4}{7} \\\\\implies \dfrac{11-4}{7} \\\\\implies \dfrac{7}{7}\!\!\!\!\!\huge{/} \\\\\bf{\implies 1}$

Formula Used:

• $\cos(90-\theta) = \sin\theta$
• $\tan(90-\theta) = \cot\theta$
• $\cos\theta * \sec\theta = 1$
• $\tan\theta * \cot\theta = 1$

Learn More:

• $\sin(90-\theta) = \cos\theta$
• $\cot(90-\theta) = \tan\theta$
• $\sec(90-\theta) = \csc\theta$
• $\csc(90-\theta) = \sec\theta$
• $\sec\theta * \csc\theta = 1$

Hope it helps!