In-AB-C-cos-2-A-cos-2-B-cos-2-C-1-Prove-that-AB-C-is-right-angled-

Question Number 164339 by mnjuly1970 last updated on 16/Jan/22

I n A \overset{Δ}{B C} : {c o s}^{2} (A) + {c o s}^{2} (B) + {c o s}^{2} (C) = 1 .

P r o v e t h a t A \overset{Δ}{B C} i s r i g h t a n g l e d .

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Answered by mindispower last updated on 17/Jan/22

{c o s}^{2} (c) - 1 = - {s i n}^{2} (A + B)

= - {s i n}^{2} (A) {c o s}^{2} (B) - {s i n}^{2} (B) {c o s}^{2} (A) - \frac{s i n (2 A) s i n (2 B)}{2}

{c o s}^{2} (A) + {c o s}^{2} (B) - {s i n}^{2} (A) {c o s}^{2} (B) - {s i n}^{2} (B) {c o s}^{2} (A) - = 0

\Leftrightarrow 2 {c o s}^{2} (A) {c o s}^{2} (B) - 2 s i n (A) s i n (B) c o s (A) c o s (B) = 0

c o s (A) c o s (B) (c o s (A + B)) = 0

c o s (A) = 0 \Rightarrow A = \frac{π}{2}, O r c o s (B) = 0 \Rightarrow B = \frac{π}{2}

A + B = \frac{π}{2} \Rightarrow C = π - (A + B) = \frac{π}{2}

Commented by mnjuly1970 last updated on 18/Jan/22

I n A \overset{Δ}{B C} : {c o s}^{2} (A) + {c o s}^{2} (B) + {c o s}^{2} (C) = 1 .

P r o v e t h a t A \overset{Δ}{B C} i s r i g h t a n g l e d .

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t h a n k y o u v e r y m u c h s i r \dots

g r a t e f u l

Commented by mindispower last updated on 19/Jan/22

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