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TS EAMCET 5 May 2018 Shift 1 Solved Paper

Section: Mathematics

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Question : 65 of 160

Marks: +1, -0

If sinh x =

\frac{3}{4}

\frac{5}{3}

then x + y =

log 2
log 6
log 3
log 5

Solution:

The value of x is expressed as,

\sinh x = \frac{3}{4}

x = \sinh^{-1} \left( \frac{3}{4} \right)

From,

\sinh^{-1} x = \log \left( x + \sqrt{x^{2}+1} \right)

x = \log \left( \frac{3}{4} + \sqrt{ \left( \frac{3}{4} \right)^{2} + 1 } \right)

= \log 2

The value of

y

is expressed as,

\cosh y = \frac{5}{3}

y = \cosh^{-1} \left( \frac{5}{3} \right)

From,

\cosh^{-1} x = \log \left( x + \sqrt{x^{2}-1} \right)

y = \log \left( \frac{5}{3} + \sqrt{ \left( \frac{5}{3} \right)^{2} - 1 } \right)

= \log 3

The value of

x+y

is,

x+y = \log 2 + \log 3

= \log 6

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