The value of -4-2-13-

The correct option is B 7 We have 2^ 13 #160; =^ 1(3^2 12×3) =^ 1(43) (π/4 2^ 13) =(π/4 ^ 14/3) =π/4.4/3+14/3 π/4 =73 ...

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Byju's Answer

Standard XII

Mathematics

Differentiation of Inverse Trigonometric Functions

The value of ...

Question

The value of $cot (\frac{π}{4} - 2 {cot}^{- 1} 3) =$

6

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Solution

The correct option is B $7$
We have $2 {cot}^{- 1} 3$

$= {cot}^{- 1} (\frac{3^{2} - 1}{2 \times 3})$

$= {cot}^{- 1} (\frac{4}{3})$

$cot (\frac{π}{4} - 2 {cot}^{- 1} 3)$
$= cot (\frac{π}{4} - {cot}^{- 1} \frac{4}{3})$

$= \frac{cot \frac{π}{4} . \frac{4}{3} + 1}{\frac{4}{3} - cot \frac{π}{4}}$

$= \frac{\frac{7}{3}}{\frac{1}{3}} = 7$

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Similar questions

Q. Find the value of:

(1) 3⁶
(2) 6³
(3) 2⁶
(4) 1⁸
(5) 5⁴
(6) 4³
(7) 10⁵
(8) 10⁷
(9) 7⁴
(10) 8²

Verify the following :

(i) $\frac{3}{7} \times (\frac{5}{6} + \frac{12}{13}) = (\frac{3}{7} \times \frac{5}{6}) + (\frac{3}{7} \times \frac{12}{13})$
(ii) $\frac{- 15}{4} \times (\frac{3}{7} + \frac{- 12}{5}) = (\frac{- 15}{4} \times \frac{3}{7}) + (\frac{- 15}{4} \times \frac{- 12}{5})$
(iii) $(\frac{- 8}{3} + \frac{- 13}{12}) \times \frac{5}{6} = (\frac{- 8}{3} \times \frac{5}{6}) + (\frac{- 13}{12} \times \frac{5}{6})$
(iv) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$