Correct Answer:
Option C - tan3θ.tan7θ = 1 (where7θ is an acute angle)
tan7θ = cot3θ
tan7θ = tan(90° – 3θ)
7θ= 90° – 3θ
then (3θ+7θ) = 90°
10θ = 90°
θ = 9°
then cot 15θ
cot (15 x 9)°
= cot 135°
= cot (90x1+45°) = – tan 45°
= –1
C. tan3θ.tan7θ = 1 (where7θ is an acute angle)
tan7θ = cot3θ
tan7θ = tan(90° – 3θ)
7θ= 90° – 3θ
then (3θ+7θ) = 90°
10θ = 90°
θ = 9°
then cot 15θ
cot (15 x 9)°
= cot 135°
= cot (90x1+45°) = – tan 45°
= –1