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Prove that :- 2cos(45°/4) = √2+√2+√2

Prove that :- 2cos(45°/4) = √2+√2+√2

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Grade:11

2 Answers

Lab Bhattacharjee
121 Points
7 years ago
\text{HINT: Use } \cos2A=2\cos^2A-1\iff\\cos A=\pm\sqrt{\dfrac{1+\cos2A}2} \text{ twice} \\ \text{Now, } 0^\circ<\dfrac{45^\circ}4<90^\circ \implies\cos\dfrac{45^\circ}4>0
Raghu Vamshi Hemadri
72 Points
7 years ago
\text{HINT: Use } \cos2A=2\cos^2A-1\iff\\cos A=\pm\sqrt{\dfrac{1+\cos2A}2} \text{ twice} \\ \text{Now, } 0^\circ<\dfrac{45^\circ}4<90^\circ \implies\cos\dfrac{45^\circ}4>0

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