Question 56

Which of the following values suits for A to make the equation $$\frac{A \tan 62^\circ \sec 28^\circ \cot 38^\circ}{\cosec 62^\circ \tan 11^\circ } = 1$$ true?

Solution

$$\frac{A \tan 62^\circ \sec 28^\circ \cot 38^\circ}{\cosec 62^\circ \tan 11^\circ } = 1$$

$$=$$>  $$\frac{A\tan62^{\circ}\sec\left(90-68\right)^{\circ}\cot38^{\circ}}{\operatorname{cosec}62^{\circ}\tan11^{\circ}}=1$$

$$=$$>  $$\frac{A\tan62^{\circ}\operatorname{cosec}62^{\circ}\cot38^{\circ}}{\operatorname{cosec}62^{\circ}\tan11^{\circ}}=1$$

$$=$$>  $$\frac{A\tan62^{\circ}\cot38^{\circ}}{\tan11^{\circ}}=1$$

$$=$$>  $$A=\frac{\tan11^{\circ\ }}{\tan62^{\circ\ }\cot38^{\circ\ }}$$

$$=$$>  $$A=\frac{\cot62^{\circ\ }\tan38^{\circ\ }}{\cot11^{\circ\ }}$$

$$=$$>  $$A=\frac{\cot\left(90-28\right)^{\circ\ }\tan38^{\circ\ }}{\cot\left(90-79\right)^{\circ\ }}$$

$$=$$>  $$A=\frac{\tan28^{\circ\ }\tan38^{\circ\ }}{\tan79^{\circ\ }}$$

Hence, the correct answer is Option C


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