If 0 < a , b < 1 , and tan - 1 a + tan - 1 b = π 4 , then the value of a + b - a 2 + b 2 2 + a 3 + b 3 3 - a 4 + b 4 4 + … is :

Question

If 0 &#60; a , b &#60; 1 , and tan - 1 a + tan - 1 b = &#960; 4 , then the value of a + b - a 2 + b 2 2 + a 3 + b 3 3 - a 4 + b 4 4 + &#8230; is :

Aicharya · Accepted Answer

tan - 1 a + tan - 1 &#160; b = &#960; 4 &#160; 0 &#60; a , b &#60; 1 &#8658; a + b 1 - a b = 1 a + b = 1 - a b a + 1 b + 1 = 2 Now a - a 2 2 + a 3 3 + &#8230; + b - b 2 2 + b 3 3 + &#8230; = log e 1 + a + log e 1 + b ( &#8757; expansion of log e 1 + x ) = log e 1 + a 1 + b = log e 2

If 0 < a , b < 1 , and tan - 1 a + tan - 1 b = π 4 , then the value of a + b - a 2 + b 2 2 + a…

Solution

If 0 &#60; a , b &#60; 1 , and tan - 1 a + tan - 1 b = &#960; 4 , then the value of a + b - a 2 + b 2 2 + a…

Solution

If 0 < a , b < 1 , and tan - 1 a + tan - 1 b = π 4 , then the value of a + b - a 2 + b 2 2 + a…