question_answer

What is the value of \[\left( co{{s}^{2}}\text{ }67{}^\circ -si{{n}^{2}}23{}^\circ  \right)\]? 

Answer:

We have, \[co{{s}^{2}}67{}^\circ -si{{n}^{2}}23{}^\circ \]

\[=co{{s}^{2}}67{}^\circ -co{{s}^{2}}\left( 90{}^\circ -23{}^\circ  \right)\]

[\[\because \]\[sin\left( 90{}^\circ -\theta  \right)=cos\theta \]]

\[=co{{s}^{2}}67{}^\circ -co{{s}^{2}}67{}^\circ \] \[=0\]