If two angles of a triangle are tan-12 and tan-13, then the third angle is
π2
π4
tan-13
None of these
Explanation for the correct answer:
Finding the third angle:
The sum of all interior angles of a triangle is π. then
A+B+C=π
Here, tan-12=A and tan-13=B
Now,
C+tan-12+tan-13=π⇒C+tan-12+31-3×2=π[∵tan-1x+tan-1y=tanx+y1-xy]⇒C+tan-1-1=π⇒C+tan-1tanπ-π4=π⇒C+π-π4=π⇒C=π4
Hence, the correct option is B.