If m sin\(\theta \) = n sin (\(\theta \) + 2\(\alpha \)), then prove that tan (\(\theta \) + \(\alpha \)) cot \(\alpha \) = \(\frac { m+n }{ m-n } \)

2

(a)

In \(\triangle \)ABC, if a cos A=b cos B, show that the triangle is either isosceles or right angled.

2

(a)

In a ΔABC, \(\frac { { a }^{ 2 }-{ b }^{ 2 } }{ { a }^{ 2 }+{ b }^{ 2 } } =\frac { \sin { \left( A-B \right) } }{ \sin { A+B } } \) , prove that it is either a right angled or an isosceles triangle.

2

(a)

Prove that
\(tan\quad \theta \quad tan\quad ({ 60 }^{ o }-\theta )tan\quad ({ 60 }^{ o }+\theta )\quad =\quad tan\quad 3\theta .\)

2

(a)

If cos \(\alpha \) +cos \(\beta\) = 0 = sin \(\alpha \) +sin\(\beta\), then find the value of cos2\(\alpha \)+cos 2\(\beta\)

2

(a)