Question

Write the function tan^−1(cosx−sinx/cosx+sinx),0

Answer 1

solution

tan∧-1(cosx-sinx)/(cosx+sinx)

=tan∧-1((cosx-sinx)(cosx-sinx)/(cosx+sinx)(cosx+sinx))

by taking the conjugate of (cosx+sinx)

⇒=tan∧-1(cos²x-2sinxcosx+sin²x)/(cos²x+2sinxcosx+sin²x)

=tan∧-1(-2sinxcosx+1)/(2sinxcosx+1)

=tan∧-1(-1)