If $\sec x=\frac{25}{24}$ and $x$ lies in first quadrant, then $\sin \frac{x}{2}+\cos \frac{x}{2}=$

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Aicharya · Accepted Answer

We have $\cos x=\frac{24}{25} \Rightarrow \sin x=\frac{7}{25} \ldots\left[\because xight.$ lies in $1^{	ext {st }}$ quadrant $]$ Also $\left(\sin \frac{x}{2}+\cos \frac{x}{2}ight)^2=1+\sin x=1+\frac{7}{25}=\frac{32}{25}$ $	herefore \sin \frac{x}{2}+\cos \frac{x}{2}=\sqrt{\frac{32}{25}}=\frac{4 \sqrt{2}}{5}=\frac{8}{5 \sqrt{2}}$

If $\sec x=\frac{25}{24}$ and $x$ lies in first quadrant, then $\sin \frac{x}{2}+\cos \frac{x}{2}=$

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