Question

In $\Delta \,\,ABC$ if $si{{n}^{2}}A+si{{n}^{2}}B+si{{n}^{2}}C=2,$ then the triangle is

• A. right angled, but need not be isosceles
• B. right angled and isosceles
• C. isosceles, but need not be right angled
• D. equilateral

Answer 1

Answer: (A)

right angled, but need not be isosceles

Answer 2

Given, ${{\sin }^{2}}A+{{\sin }^{2}}B+{{\sin }^{2}}C=2$
$\Rightarrow$ $1-{{\cos }^{2}}A+1-{{\cos }^{2}}B+1-{{\cos }^{2}}C=2$
$\Rightarrow$ $1={{\cos }^{2}}A+{{\cos }^{2}}B+{{\cos }^{2}}C$
$\Rightarrow$ $1=1-2\cos A\,\cos B\,\cos C$
$\Rightarrow$ $\cos A\,\cos B\,\cos \,C=0$
At least one angle should be ${{90}^{o}}$ and sum of two angles should be ${{90}^{o}}$ .
Hence, option [a] is correct.