Question

tan(π/4 + 1/2 cos^-1 x) +
tan (π/4 - 1/2 cos^-1 x)equals.

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Answer 1

Step-by-step explanation:

tan(π/4 + 1/2 cos^-1 x) +

tan (π/4 - 1/2 cos^-1 x)equals.

Answer 2

Answer :

We have,

$tan (π/4 + 1/2 cos^ - 1 x) + \\ tan (π/4 - 1/2 cos^ - 1 x)$

$Let \: cos {}^{ - 1} x = t = > x \: cos \: t.$

$=> tan (x/4 + t/2) + tan (x/4 - t/2)$

$= tan (π/4) + tan (t/2) / 1 - tan(π/4) tan (t/2) + \\ </u></strong></p><p><strong><u>[tex]= tan (π/4) + tan (t/2) / 1 - tan(π/4) tan (t/2) + \\ tan (π/4) - tan (t/2) / 1 + tan (π/4) tan ( t/2)$

$= 1 + tan(t/2) / 1 - tan (t/2) + </u></strong></p><p><strong><u>[tex]= 1 + tan(t/2) / 1 - tan (t/2) + \\ 1 - tan (t/2) /1+ tan(t/2) </u></strong></p><p><strong><u>[tex]= 1 + tan(t/2) / 1 - tan (t/2) + \\ 1 - tan (t/2) /1+ tan(t/2)$

$= [ 1 + tan (t/2) ]^2 + [ 1 - tan (t/2) ]^2 / \\ (1 - tan (t/2)) ( 1 + tan (t/2))$

$= 2 (1 + tan^2 ( t /2)) / 1 - tan^2 ( t/2)$

$= 2/ cos t$

$Answer \: ⟿ = 2/x$

Step-by-step explanation:

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