Question

Write ‘True’ or ‘False’ and justify your answer. The value of the expression (cos2 23° – sin2 67°) is positive

NCERT Class X
Mathematics - Exemplar Problems

Chapter _INTRODUCTION TO TRIGONOMETRY AND ITS APPLICATIONS

Answer 1

$\textbf{Given:}$

$cos^223^{\circ}-sin^267^{\circ}$

$\text{Using}$

$\bf\,sin\theta=cos(90^{\circ}-\theta)$

$\implies\,sin\,67^{\circ}=cos\,23^{\circ}$

$\text{Now,}$

$cos^223^{\circ}-sin^267^{\circ}$

$=cos^223^{\circ}-cos^223^{\circ}$

$=0$

$\text{Hence the statement}\;cos^223^{\circ}-sin^267^{\circ}\;\text{is positive is not true}$