Question

find x if 4sin inverse x= π- cos inverse x​

Answer 1

Answer:

Given: 4sin

−1

x+cos

−1

x=π

We know that sin

−1

x+cos

−1

x=

2

π

⇒cos

−1

x=

2

π

−sin

−1

x

Now we have,

4sin

−1

x+cos

−1

x=π

⇒4sin

−1

x+

2

π

−sin

−1

x=π

⇒3sin

−1

x=π−

2

π

⇒3sin

−1

x=

2

2π−π

⇒3sin

−1

x=

2

π

⇒sin

−1

x=

6

π

⇒x=sin(

6

π

)=

2

1

∴x=

2

1

Answere

Step-by-step explanation:

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Answer 2

ㅤ$\;\;\underline{\textbf{\textsf{Given:-}}}$

• $\rm{4{\sin}^{-1}x=\pi-{\cos}^{-1}x}$

ㅤ$\;\;\underline{\textbf{\textsf{ To Find:-}}}$

• Value of x

ㅤ$\;\;\underline{\textbf{\textsf{Solution :-}}}$

Given that,

• $\rm{4{\sin}^{-1}x=\pi-{\cos}^{-1}x}$

$\underline{\:\textsf{ We know that :}}$

$\rm{{\sin}^{-1}x+{\cos}^{-1}x=\dfrac{\pi}{2}}$

$\underline{\:\textsf{ Then :}}$

$\dashrightarrow \rm{4{\sin}^{-1}x=\pi-(\dfrac{\pi}{2}-{\sin}^{-1}x)}$

$\dashrightarrow \rm{4{\sin}^{-1}x=\pi-\dfrac{\pi}{2}+{\sin}^{-1}x)}$

$\dashrightarrow \rm{4{\sin}^{-1}x-{\sin}^{-1}x=\pi-\dfrac{\pi}{2}}$

$\dashrightarrow \rm{3{\sin}^{-1}x=\dfrac{\pi}{2}}$

$\dashrightarrow \rm{{\sin}^{-1}x=\dfrac{\pi}{6}}$

$\dashrightarrow \rm{\sin\dfrac{\pi}{6}=x}$

$\dashrightarrow \rm{x=\dfrac{1}{2}}$

ㅤ$\;\;\underline{\textbf{\textsf{ Hence-}}}$

$\underline{\textsf{ Value of x is \textbf{ 1/2 or, 0.5 }}}.$

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ㅤ$\;\;\underline{\textbf{\textsf{ Need to Know -}}}$

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

$2)\rm{{\tan}^{-1}x+{\cot}^{-1}x=\dfrac{\pi}{2}}$

$3)\rm{{\sec}^{-1}x+{\cosec}^{-1}x=\dfrac{\pi}{2}}$

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