Question

If 3 sin-1x + cos-1x = π, then x is equal to

Answer 1

Answer:

x=0.5

Step-by-step explanation:

As we know sin^-1x + cos^-1x is π÷2

4 sin^-1x can be written as 3 sin inverse x + sin inverse x

Therefore 4 sin inverse x + cos inverse x can be written as 3 sin inverse x + sin inverse x +cos inverse x=π

which will be 3 sin inverse x +π÷2=π

=>3 sin inverse x = π÷2

=>sin inverse x =π÷6

x=1÷2 or x=0.5

hope it is helpful, please mark as brainliest

Answer 2

Answer:

The value if x is

$x = \frac{1}{ \sqrt{2} }$

Step-by-step explanation:

The given inverse trigonometric equation is

$3 \sin {}^{ - 1} (x) + \cos {}^{ - 1} (x) = \pi$

We have an inverse trigonometric identity which is

$\sin {}^{ - 1} (x) + \cos {}^{ - 1} (x) = \frac{\pi}{2}$

Our given inverse trigonometric equation can be reframed as

$\\ 2 \sin {}^{ - 1} (x) + ( \sin {}^{ - 1} (x) + \cos {}^{ - 1} (x) ) = \pi$

Substituting the given trigonometric identity in the above expression we get

$2 \sin {}^{ - 1} (x) + \frac{\pi}{2} = \pi \\ = > 2 \sin {}^{ - 1} (x) = \frac{\pi}{2} \\ = > \sin {}^{ - 1} (x) = \frac{\pi}{4}$

Hence the value of x is

$x = \sin( \frac{\pi}{4} ) = \frac{1}{ \sqrt{2} }$

#SPJ3