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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