58. In an acute-angled triangle ABC, if tan(A+ B-C) = 1and sec(B + C-A

1.	58. In an acute-angled triangle ABC, if tan(A+ B-C) = 1and sec(B + C-A)= 2 , find the value of A, B and C
Answer» From question,tan(theta¹)=1.So, theta¹=45°sec(theta²)=2So,theta²=60° A+B-C=45° .......eq(1)B+C-A=60° .......eq(2)ALSO, A+B+C=180°.....eq(3) NOW, ADDING eq(1) & eq(2) 2(B)=105B=52.5° ADDING eq(1) & eq(3) 2(A+B)=225°A=112.5°-52.5°A=60° now adding eq(2) & eq(3) 2(B+C)=240C=120°-52.5°C=67.5°

58. In an acute-angled triangle ABC, if tan(A+ B-C) = 1and sec(B + C-A)= 2 , find the value of A, B and C

Answer»

From question,tan(theta¹)=1.So, theta¹=45°sec(theta²)=2So,theta²=60°

A+B-C=45° .......eq(1)B+C-A=60° .......eq(2)ALSO, A+B+C=180°.....eq(3)

NOW, ADDING eq(1) & eq(2) 2(B)=105B=52.5°

ADDING eq(1) & eq(3) 2(A+B)=225°A=112.5°-52.5°A=60°

now adding eq(2) & eq(3) 2(B+C)=240C=120°-52.5°C=67.5°