show that tan^-1v+cot^-1v=pie/2

Question

can you give me an example of how to solve this step by step

Answer 1

Hello Joseph,

 

Here is how  to proceed,

 

Sin^-1q = Q  means that SinQ = q, where Q is the angle in degrees or radians and q is a ratio

 

You need to Prove that two angles add up to Pi/2

 

tan^-1v + cot^-1v = Pi/2

 

let A = tan^-1v then tanA = v      

let B = cot^-1v then cotB =v                               

                              

Since both of these quantities equal to v, they must equal each other

 

tanA = cot B                                         sinA/cosA = tanA and cosB/sinB = cotB

 

so

 

sinA/cosA= cosB/sinB

sinAsinB =cosBcosA

sinAsinB - cosBcosA = 0

cos(A + B) = 0

 A + B = cos^-10

A  + B = pi/2  now plug in   A =tan^-1v and B = cot^-1v