Question

cos {2sin inverse (-x) } = 0 find the value of x​

Answer 1

Answer:

cos(2sin^-1x)=1-2x^2.

cos

(

2

sin

−

1

x

)

=

1

−

2

x

2

.

Explanation:

Let sin^-1x=theta

sin

−

1

x

=

θ

, so that, x=sintheta, |x|<=1, theta in [-pi/2,pi/2].

x

=

sin

θ

,

|

x

|

≤

1

,

θ

∈

[

−

π

2

,

π

2

]

.

Now, Reqd. Value = cos(2sin^-1x)=cos2theta=1-2sin^2theta=1-2x^2.

=

cos

(

2

sin

−

1

x

)

=

cos

2

θ

=

1

−

2

sin

2

θ

=

1

−

2

x

2

.

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