If sin x + sin y = a and cos x + cos y = b, then ${\tan ^2}\left( {\frac{{{\rm{x}} + {\rm{y}}}}{2}} \right) + {\tan ^2}\left( {\frac{{{\rm{x}} - {\rm{y}}}}{2}} \right)$ is equal to

Question

If sin x + sin y = a and cos x + cos y = b, then ${\tan ^2}\left( {\frac{{{\rm{x}} + {\rm{y}}}}{2}} \right) + {\tan ^2}\left( {\frac{{{\rm{x}} - {\rm{y}}}}{2}} \right)$ is equal to

TuteeHUB · Accepted Answer

$\frac{{{{\rm{a}}^4} - {{\rm{b}}^4} + 4{{\rm{a}}^2}}}{{{{\rm{a}}^2}{{\rm{b}}^2} + {{\rm{a}}^4}}}$

TuteeHUB · Answer

$\frac{{{{\rm{a}}^4} + {{\rm{b}}^4} + 4{{\rm{b}}^2}}}{{{{\rm{a}}^2}{{\rm{b}}^2} + {{\rm{b}}^4}}}$

TuteeHUB · Answer

$\frac{{{{\rm{a}}^4} - {{\rm{b}}^4} + 4{{\rm{b}}^2}}}{{{{\rm{a}}^2}{{\rm{b}}^2} + {{\rm{b}}^4}}}$

TuteeHUB · Answer

None of the above

1.	If sin x + sin y = a and cos x + cos y = b, then \({\tan ^2}\left( {\frac{{{\rm{x}} + {\rm{y}}}}{2}} \right) + {\tan ^2}\left( {\frac{{{\rm{x}} - {\rm{y}}}}{2}} \right)\) is equal to
A.	\(\frac{{{{\rm{a}}^4} + {{\rm{b}}^4} + 4{{\rm{b}}^2}}}{{{{\rm{a}}^2}{{\rm{b}}^2} + {{\rm{b}}^4}}}\)
B.	\(\frac{{{{\rm{a}}^4} - {{\rm{b}}^4} + 4{{\rm{b}}^2}}}{{{{\rm{a}}^2}{{\rm{b}}^2} + {{\rm{b}}^4}}}\)
C.	\(\frac{{{{\rm{a}}^4} - {{\rm{b}}^4} + 4{{\rm{a}}^2}}}{{{{\rm{a}}^2}{{\rm{b}}^2} + {{\rm{a}}^4}}}\)
D.	None of the above
Answer» C. \(\frac{{{{\rm{a}}^4} - {{\rm{b}}^4} + 4{{\rm{a}}^2}}}{{{{\rm{a}}^2}{{\rm{b}}^2} + {{\rm{a}}^4}}}\)

If sin x + sin y = a and cos x + cos y = b, then \({\tan ^2}\left( {\frac{{{\rm{x}} + {\rm{y}}}}{2}} \right) + {\tan ^2}\left( {\frac{{{\rm{x}} - {\rm{y}}}}{2}} \right)\) is equal to

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