CBSE Class 10 Maths Question Paper 2018 | Q19B

Question 19B: If tan 2A = cot (A - 18°), where 2A is an acute angle, find the value of A.

Video Explanation

Explanatory Answer | CBSE 2018 Board Paper Q19B

2A is an acute angle. So, A will be an acute angle.
Hence, (A - 18°) will also be an acute angle.
∴ A and (A - 18°) are acute angles.

Because 2A and (A - 18°) are acute, tan 2A and cot (A - 18°) will be positive as they are in the First Quadrant.

Trigonometric ratio of complementary angles: tan θ = cot(90° - θ)
tan 2A = cot (90° - 2A)
i.e., cot (90 - 2A) = cot (A - 18°)
∴ 90° - 2A = A - 18°
108° = 3A
Or ∠A = 36°