If A, B and C are the interior angles of a right-angle triangle, right-angled at B then find the value of A, given that tan2A=cot(A–30∘) and 2A is an acute angle.
Using the trigonometric ratio of complementary angles,
cot(90∘−A)=tanA
From this ratio, we can write the above expression as:
⇒tan2A=cot(90∘−2A) ….(1)
Given expression is tan2A=cot(A–30∘) ….(2)
Now, equate the equation (1) and (2), we get
cot(90∘−2A)=cot(A–30∘)
⇒90∘−2A=A–30∘
⇒3A=90∘+30∘
⇒3A=120∘
⇒A=120∘3
⇒A=40∘
Thus, the measure of the acute angle A can be easily calculated by making use of the trigonometry ratio of complementary angles.