If in a ∆ABC, A=tan-12 and B=tan-13, then angle C is
π2
π3
π4
None of these.
Explanation for the correct option.
Find the angle C:
Given,
A=tan-12 and B=tan-13.
In a triangle ∠A+∠B+∠C=π.
∠A+∠B+∠C=π⇒tan-12+tan-13+∠C=π⇒tan-12+31-2×3+∠C=π[∵tan-1x+tan-1y=π-tan-1x+y1-xy,xy>1]⇒π-tan-15-5+∠C=π⇒π-tan-1-1+∠C=π⇒π-π4+∠C=π[∵tan-1(-1)=-π4]⇒∠C=π4
Hence, the correct option is C.