Evaluate \(\frac { tan{ 65 }^{ o } }{ tan{ 25 }^{ o } } \)

Express cot 85° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.

If ATB=90^o then prove that
\(\sqrt { \frac { tanA\quad tanB+tanA\quad cotB }{ sinA\quad secB } } -\frac { { Sin }^{ 2 }A }{ { Cos }^{ 2 }A } =tanA\)

If 15tan² θ+4 sec² θ=23 then find the value of (secθ+cosecθ)² -sin² θ

If tanθ+sinθ=P; tanθ-sinθ=q P.T P²-q²=4\(\sqrt{pq}\)