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Introduction of Trigonometry — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsIntroduction of Trigonometry1 Mark
Question
Write 'True' or 'False' and justify your answer.
The value of the expression $\left(\cos ^2 23^{\circ}-\sin ^2 67^{\circ}\right)$ is positive.
✓

Answer

False. $23^{\circ}$ and $67^{\circ}$ are complementry angles so.
$\cos ^2 23^{\circ}-\sin ^2 67^{\circ}=\cos ^2 23^{\circ}-\sin ^2\left(90^{\circ}-23^{\circ}\right)$
$=\cos ^2 23^{\circ}-\cos ^2 23^{\circ}$
$=0$
So, the value of the given expression is not positive. Hence, the given statement is false.

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