in triangle ABC, if cos A = sin B - cos C then show that it is a right angled - Maths -

Question

in triangle ABC, if cos A = sin B - cos C then show that it is a
right angled triangle

Shruti Tyagi · Accepted Answer

Dear student,

Given: cosA= sinB- cosC  ⇒cosA+cosC=sinB  ⇒2cosA+C2
 cosA-C2  =sin180-(A+C)⇒2cosA+C2
 cosA-C2 =sin(A+C)⇒2cosA+C2
 cosA-C2 =2sinA+C2cosA+C2⇒cosA-C2=sinA+C2⇒cosA-C2=  cos90-A+C2 ⇒A-C2=90 -A+C2⇒ A-C=180-(A+C) ⇒ A-C=180-A-C ⇒ 2A=180  ⇒A=90Thus, ∆ABC is right angled triangle

Regards

in triangle ABC, if cos A = sin B - cos C then show that it is a right angled triangle.