Find m if tan - 1 1-x2 - 1-1x- m-4- x - - 1-

tan^ 11√(x^2 1)+ ^ 1 x = mπ4 Let x = θ . tan^ 11√(^2 θ 1)+ ^ 1 (θ) = m π4 tan^ 11tanθ + θ = m π4 tan^ 1 (θ) + θ = mπ4 tan^ 1(tan{π2 ...

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Standard XII

Mathematics

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Find m if t...

Question

Find m if ${tan}^{- 1} \frac{1}{\sqrt{x^{2} - 1}} + {sec}^{- 1} x = \frac{m π}{4}, | x | > 1$ .

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Solution

${tan}^{- 1} \frac{1}{\sqrt{x^{2} - 1}} + {sec}^{- 1} x = \frac{m π}{4}$

Let $x = sec θ$ .

${tan}^{- 1} \frac{1}{\sqrt{{sec}^{2} θ - 1}} + {sec}^{- 1} (sec θ) = \frac{m π}{4}$

${tan}^{- 1} \frac{1}{tan θ} + θ = \frac{m π}{4}$

${tan}^{- 1} (cot θ) + θ = \frac{m π}{4}$

${tan}^{- 1} (tan {\frac{π}{2} - θ}) + θ = \frac{m π}{4}$ .

$\frac{π}{2} - θ + θ = \frac{m π}{4}$

we get $\frac{m π}{4} = \frac{π}{2}$

$∴ m = 2$

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(viii) tan (cos⁻¹x) = sin $(\cot^{- 1} \frac{1}{2})$

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{t a n}^{- 1} (x - 1) + {t a n}^{- 1} x + {t a n}^{- 1} (x + 1) = {t a n}^{- 1} 3 x

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Find m if tan−11√x2−1+sec−1x=mπ4,|x|>1.

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Find m if ${tan}^{- 1} \frac{1}{\sqrt{x^{2} - 1}} + {sec}^{- 1} x = \frac{m π}{4}, | x | > 1$ .