# $$\frac{3 \tan^2 60^{\circ}+ \sec^2 30^{\circ}- \sin^2 45^{\circ}}{(\cos 15^{\circ}+ \sin 75^{\circ})(\sec15^{\circ}+ cosec 75^{\circ})}$$ का मान क्या है?

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SSC CHSL 2020 Official Paper 20 ( Held on: 5 Aug 2021 Shift 2)
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1. $$\frac{13}{12}$$
2. $$\frac{5}{12}$$
3. $$\frac{65}{24}$$
4. $$\frac{59}{24}$$

Option 4 : $$\frac{59}{24}$$
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## Detailed Solution

दिया गया है:

$$\frac{3 \tan^2 60^{\circ}+ \sec^2 30^{\circ}- \sin^2 45^{\circ}}{(\cos 15^{\circ}+ \sin 75^{\circ})(\sec15^{\circ}+ cosec 75^{\circ})}$$

प्रयुक्त अवधारणा:

गणना:

$$\frac{3 \tan^2 60^{\circ}+ \sec^2 30^{\circ}- \sin^2 45^{\circ}}{(\cos 15^{\circ}+ \sin 75^{\circ})(\sec15^{\circ}+ cosec 75^{\circ})}$$

[3 × (√3)2 + (2/√3)2 – (1/√2)2]/[{cos15° + sin(90 – 15)}{sec15° + cosec(90 - 15)}]

⇒ (3 × 3 + 4/3 – 1/2)/[(2cos15°)(2sec15°)]

⇒ [(54 + 8 - 3)/6]/[(2cos15°)(2/cos15°)]

⇒ 59/24

∴ अभीष्ट उत्तर 59/24 है।
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