Question

Prove that.
2tan⁻¹(1/3) = tan⁻¹(3/4)

Answer 1

As we know that

$2 {tan}^{ - 1} x = {tan}^{ - 1} ( \frac{2x}{1 - {x}^{2} } ) \\ \\so \\ 2 {tan}^{ - 1}( \frac{1}{3} ) = {tan}^{ - 1} ( \frac{2 \times \frac{1}{3} }{1 - ({ \frac{1}{3} )}^{2} } ) \\ \\ = {tan}^{ - 1} ( \frac{ \frac{2}{3} }{ \frac{8}{9} } ) \\ \\ = {tan}^{ - 1} ( \frac{2 \times 8}{3 \times 10} ) \\ \\ = {tan}^{ - 1} ( \frac{3}{4} )$

thus it is equal to tan⁻¹(3/4)

hence proved.

Answer 2

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