Question

Prove that:

${tan}^{ - 1} \frac{1 +x }{ 1 - x}$
equal to
$\frac{\pi}{4} + {tan}^{ - 1} x$
​

Answer 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