Solve inverse trigonometric equation &#x03C0;<!-- π --> 6 </mfrac> = t

Davon Irwin

Davon Irwin

Answered question

2022-06-14

Solve inverse trigonometric equation π 6 = tan 1 11 x tan 1 1 x

Answer & Explanation

Bornejecbo

Bornejecbo

Beginner2022-06-15Added 19 answers

30 = tan 1 11 x tan 1 1 x
Take the tan of both sides
tan 30 = tan ( tan 1 11 x tan 1 1 x )
Angle addition - subtraction rule for tangent
tan ( A + B ) = tan A + tan B 1 tan A tan B tan ( A B ) = tan A tan B 1 + tan A tan B
1 3 = tan ( tan 1 11 x ) tan ( tan 1 1 x ) 1 + tan ( tan 1 11 x ) tan ( tan 1 1 x )
tan ( tan 1 y ) = y
1 3 = 11 x 1 x 1 + 11 x 2
Multiply numerator and denominator by x 2 to kill the fractions.
1 3 = 10 x x 2 + 11
1 3 = 10 x x 2 + 11
Use the quadratic formula:
x = 5 3 ± 75 11 x = 5 3 ± 8

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