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Flag Trigonometry> Solve the equation: cos⁻¹[√(6)x] + cos⁻¹[...
question mark

Solve the equation:
cos⁻¹[√(6)x] + cos⁻¹[3√(3) x²]=π/2

Sarvesh , 6 Years ago
Grade 12
anser 1 Answers
Samyak Jain

Last Activity: 6 Years ago

cos–1(\sqrt{6} x) + cos–1(3\sqrt{3} x²) = π/2       ….(1)
We know that cos–1(u) = sin–1(\sqrt{1-u^2})
So, cos–1(\sqrt{6} x) = sin–1(\sqrt{1-6x^2})
\therefore (1) becomes sin–1(\sqrt{1-6x^2}) + cos–1(3\sqrt{3} x²) = π/2
Also sin–1(u) + cos–1(u) = π/2.  \Rightarrow  \sqrt{1-6x^2}  =  3\sqrt{3} x²
i.e. 1 – 6x2 = 27 x4    or   27 x4 + 6x2 – 1 = 0
(3x2 + 1)(9x2 – 1) = 0
x2 = 1/9.       Here x2 cannot be –1/3.
x = \pm 1/3      But x = –1/3 is not satisfied by the given equation.
\therefore x = 1/3 is the solution.
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