If \tan 4A = \cot (A - 20^\circ), 0^\circ < 4A < 90^\circ , then the value of A is:

Question 67

If $$\tan 4A = \cot (A - 20^\circ), 0^\circ < 4A < 90^\circ$$ , then the value of A is:

Solution

Given, $$\tan 4A = \cot (A - 20^\circ)$$, $$0^\circ < 4A < 90^\circ$$

$$=$$> $$\cot\left(90^{\circ}-4A\right)=\cot(A-20^{\circ})$$

$$=$$> $$90^{\circ}-4A=A-20^{\circ}$$

$$=$$> $$A+4A=90^{\circ}+20^{\circ\ }$$

$$=$$> $$5A=110^{\circ\ }$$

$$=$$> $$A=22^{\circ\ }$$

Hence, the correct answer is Option B

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