If x = 3   t a n t and y = 3   s e c t , then the value of d 2 y d x 2 at t = π 4 , is:

Question

If x = 3 &#160; t a n t and y = 3 &#160; s e c t , then the value of d 2 y d x 2 at t = &#960; 4 , is:

Aicharya · Accepted Answer

Given x = 3 tan t and y = 3 sec t &#8658; d x d t = 3 sec 2 t and d y d t = 3 sec t tan t &#8658; d y d x = d y d t d x d t &#8658; d y d x = sin t &#8658; d 2 y d x 2 = cos t &#183; d t d x = cos t &#160; &#183; cos 2 t 3 = cos 3 t 3 At t = &#960; 4 d 2 y d x 2 = 1 6 2

If x = 3 &#160; t a n t and y = 3 &#160; s e c t , then the value of d 2 y d x 2 at t = &#960; 4 , is:

Solution

If x = 3 t a n t and y = 3 s e c t , then the value of d 2 y d x 2 at t = π 4 , is: