Example 4 Show that in any triangle ABC,
a = b cos C + c cos B
Solution Let p be the statement “ABC is any triangle” and q be the statement
“a = b cos C + c cos B”
Let ABC be a triangle From A draw AD a perpendicular to BC (BC produced if
necessary) As we know that any triangle has to be either acute or obtuse or right angled, we
can split p into three statements r, s and t, where
Rationalised 2023-24
PROOFS IN MATHEMATICS
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r : ABC is an acute angled triangle with ∠ C is acute s : ABC is an obtuse angled triangle with ∠ C is obtuse