Verified by Ajay Kumar
If \(\sin\theta-\cos\theta=\frac45\), then find the value of \(\sin\theta+\cos\theta\).
\(\frac{\sqrt{34}}{5}\)
\(\frac{5}{\sqrt{34}}\)
\(\frac{\sqrt{24}}{5}\)
\(\frac{5}{\sqrt{24}}\)
Answer: A
Solution: Use \((\sin\theta+\cos\theta)^2+(\sin\theta-\cos\theta)^2=2\). Thus, \((\sin\theta+\cos\theta)^2=2-\frac{16}{25}=\frac{34}{25}\). Taking the positive value given in the options, \(\sin\theta+\cos\theta=\frac{\sqrt{34}}5\). Trick: Square the sum and difference; their squares add up to 2.
यदि \(\sin\theta-\cos\theta=\frac45\), तो \(\sin\theta+\cos\theta\) का मान ज्ञात कीजिए।
\(\frac{\sqrt{34}}{5}\)
\(\frac{5}{\sqrt{34}}\)
\(\frac{\sqrt{24}}{5}\)
\(\frac{5}{\sqrt{24}}\)
उत्तर: A
हल: \((\sin\theta+\cos\theta)^2+(\sin\theta-\cos\theta)^2=2\) का प्रयोग करें। इसलिए \((\sin\theta+\cos\theta)^2=2-\frac{16}{25}=\frac{34}{25}\)। विकल्पों में दिया धनात्मक मान \(\sin\theta+\cos\theta=\frac{\sqrt{34}}5\) है। ट्रिक: योग और अंतर के वर्गों का उपयोग करें; दोनों वर्गों का योग 2 होता है।
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