Evaluate 1+cos⌽1-cos⌽
Consider
1+cos⌽1-cos⌽
Multiply and divided by 1+cos⌽
1+cos⌽1-cos⌽×1+cos⌽1+cos⌽1+cos⌽212-cos⌽21+cos⌽21-cos2⌽1+cos⌽2sin2⌽21+cos⌽sin⌽21sin⌽+cos⌽sin⌽2cosec⌽+cot⌽2
Hence, 1+cos⌽1-cos⌽ is cosec⌽+cot⌽2
loge(n+1)−loge(n−1)=4a[(1n)+(13n3)+(15n5)+...∞] Find 8a.