(i) cosec(690°) = \(\frac{1}{sin(-690^\circ)}\) \(\Rightarrow\) \(\frac{1}{-sin(690^\circ)}\) = \(\frac{1}{-sin(2.360-30^\circ)}\)
……..(IV quadrant sinx is negative)
(vi) tan225° = tan(180° + 45°) …………(in III quadrant tanx is positive)
\(\Rightarrow\) tan45° = 1
(vii) cot(-315°) = \(\frac{1}{tan(-315)^\circ}\) \(\Rightarrow \frac{1}{-tan(315^\circ)}\) = \(=\frac{1}{-tan(360^\circ-45^\circ)}\)
.….(tan( - x) = - tanx)
.......(in IV quadrant tanx is negative)
(viii) sin( - 1230°) = sin1230° ………….(using sin( - x) = sinx)
= sin(3.360° + 150°)
= sin150°
= sin(180° - 30°) ………….(using sin(180° - x) = sinx)
= sin30°
= \(\frac{1}{2}\)
(ix) cos495° = cos(360° + 135°) …………(using cos(360° + x) = cosx)
= cos135°
= cos(180° - 45°) ………….(using cos(180° - x) = - cosx)
= - cos45°
= \(-\frac{1}{\sqrt{2}}\)
