Prove that:

[tex] {tan}^{ – 1} \frac{1 +x }{ 1 – x} [/tex]
equal to
[tex] \frac{\pi}{4} + {tan}^{ – 1} x[/

1 thought on “Prove that:<br /><br />[tex] {tan}^{ – 1} \frac{1 +x }{ 1 – x} [/tex]<br />equal to<br />[tex] \frac{\pi}{4} + {tan}^{ – 1} x[/”

1. Answer:

   The second and third identities can be obtained by manipulating the first. The identity 1+cot2θ=csc2θ1+cot2θ=csc2θ is found by rewriting the left side of the equation in terms of sine and cosine.

   Prove: 1+cot2θ=csc2θ1+cot2θ=csc2θ

   1+cot2θ=(1+cos2θsin2θ)Rewrite the left side. =(sin2θsin2θ)+(cos2θsin2θ)Write both terms with the common denominator. =sin2θ+cos2θsin2θ

   Reply