Simplify the expression by using a double-angle formula. \[ 2 \cos ^{2} \frac{\pi}{7}-1 \]

If the adjacent side measures 8 meters and the angle opposite to it is 45 degrees, calculate the length of the opposite side using trigonometric ratios.

एक समकोण त्रिकोण में, कोण A के लिए कोशाइन का परिभाषा बताएं।

What is the definition of the cosine function in relation to a right triangle using the adjacent side and hypotenuse?

If \( \tan \theta=\frac{20}{21} \), show that \( \frac{1-\sin \theta+\cos \theta}{1+\sin \theta+\cos \theta}=\frac{3}{7} \). (OR)

б) \( \sin ^{2} x \cdot \cos x=0 \) 2) \( \sin 3 x+\sin x=0 \)