Inverse trig

Geometry Level pending

If sin ⁡ − 1 x + sin ⁡ − 1 y + sin ⁡ − 1 z = 3 π 2 \sin^{-1} x +\sin^{-1} y + \sin^{-1} z = \dfrac {3\pi}2 , then

arcsin ⁡ ( 2017 x 2017 − 2016 x 2016 2015 x 2015 − 2017 x 2017 ) = a π b \arcsin \left( \dfrac{2017 x^{2017} - 2016x^{2016}}{2015x^{2015}-2017x^{2017}}\right) = \frac{a\pi}{b}

where a a and b b are coprime integers. Find ∣ a + b ∣ |a + b| .


The answer is 5.

Jaya Krishna by Jaya Krishna , 20, India

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1 solution

Ananya Agrahari
Jun 23, 2017

(pi/2) is the maximum value of arcsin(x), arcsin(y) & arcsin(z). So easily x=y=z=1. Now the asked value is arcsin(-1/2) so it is (-pi/6).

PS: The question must be edited because someone could consider denominator as negative so answer can also be -5

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