The value of cot -4-2cot-13 is equal to

Cot ( π/4 2cot^ 13 ) = cot [ π/4 cot^ 1 ( 3^2 1/2×3 ) ]=cot [ π/4 cot^ 14/3 ] = ( cotπ/4 )4/3+1/4/3 cotπ/4=4/3+1/4/3 1=7/1=7 nbsp; nbsp; nbsp;Use th ...

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Standard XI

Mathematics

Composition of Trigonometric Functions and Inverse Trigonometric Functions

The value of ...

Question

The value of $c o t (\frac{π}{4} - 2 c o t^{- 1} 3)$ is equal to

-7

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Solution

The correct option is B
7

$c o t (\frac{π}{4} - 2 c o t^{- 1} 3) = c o t [\frac{π}{4} - c o t^{- 1} (\frac{3^{2} - 1}{2 \times 3})] = c o t [\frac{π}{4} - c o t^{- 1} \frac{4}{3}] = \frac{(c o t \frac{π}{4}) \frac{4}{3} + 1}{\frac{4}{3} - c o t \frac{π}{4}} = \frac{\frac{4}{3} + 1}{\frac{4}{3} - 1} = \frac{7}{1} = 7$ Use the result [ $2 c o t^{- 1} x = c o t^{- 1} (\frac{x^{2} - 1}{2 x}) a n d c o t (A - B) = \frac{c o t B c o t A + 1}{c o t B - c o t A}$ ]

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The value of cot(π4−2cot−13) is equal to

The correct option is B 7 cot(π4−2cot−13)=cot[π4−cot−1(32−12×3)]=cot[π4−cot−143]=(cotπ4)43+143−cotπ4=43+143−1=71=7 Use the result [2cot−1x=cot−1(x2−12x) and cot(A−B)=cotBcotA+1cotB−cotA]

The value of $c o t (\frac{π}{4} - 2 c o t^{- 1} 3)$ is equal to