The distance of three points on a pole from its foot are in A.P. If the angles of elevation of these points from a point on the ground are α,βand γ, then $$cot$$β$$cot$$γ,$$cot$$γ$$cot$$α and $$cot$$α$$cot$$β are in

Question

The distance of three points on a pole from its foot are in A.P.  If the angles of elevation of these points from a point on the ground are α,βand γ, then $$cot$$β$$cot$$γ,$$cot$$γ$$cot$$α and $$cot$$α$$cot$$β are in

Infinity Learn · Accepted Answer

Given $$AB=a$$, $$AC=b$$, $$AD=ca$$,b,c are in A.P. ⇒$$2b=a+cAlso$$ we have $$tan$$α$$=ax$$,$$tan$$β$$=bx$$,$$tan$$γ$$=cx$$∴$$cot$$β.$$cot$$γ$$+$$$$cot$$α.$$cot$$β$$=xb$$.$$xc+xa$$.xb                                    $$=x2ba+cac=x2b.2bac$$                                      $$=2x2ac=2$$.xa.xc                                       $$=2cot$$α.$$cot$$γ

The distance of three points on a pole from its foot are in A.P. If the angles of elevation of these points from a point on the ground are $α, β$ and $γ$ , then $c o t β c o t γ, c o t γ c o t α a n d c o t α c o t β a r e i n$

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

The distance of three points on a pole from its foot are in A.P. If the angles of elevation of these points from a point on the ground are α,βand γ, then cotβcotγ,cotγcotα and cotαcotβ are in

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

The distance of three points on a pole from its foot are in A.P. If the angles of elevation of these points from a point on the ground are $α, β$ and $γ$ , then $c o t β c o t γ, c o t γ c o t α a n d c o t α c o t β a r e i n$