The value of tan - cos-1 -2-7 -2- is

Tan [ cos^ 1 ( 2/7) π/2 ]=tan [ π cos^ 1 ( 2/7 ) π/2 ]=tan [ π/2 cos^ 1 ( 2/7 ) ]=cot ( cos^ 1 ( 2/7 ) ) =cot ( cot^ 1 ( 2/√(45) ) )=2/√(45)=2/3√(5) ...

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Standard XIII

Mathematics

Properties with Negative X

The value of ...

Question

The value of $t a n [c o s^{- 1} (\frac{- 2}{7}) - \frac{π}{2}]$ is

$\frac{2}{3 \sqrt{5}}$

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$\frac{3 \sqrt{5}}{2}$

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$\frac{2}{\sqrt{5}}$

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None

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Solution

The correct option is A
$\frac{2}{3 \sqrt{5}}$

$t a n [c o s^{- 1} (\frac{- 2}{7}) - \frac{π}{2}] = t a n [π - c o s^{- 1} (\frac{2}{7}) - \frac{π}{2}] = t a n [\frac{π}{2} - c o s^{- 1} (\frac{2}{7})] = c o t (c o s^{- 1} (\frac{2}{7})) = c o t (c o t^{- 1} (\frac{2}{\sqrt{45}})) = \frac{2}{\sqrt{45}} = \frac{2}{3 \sqrt{5}}$

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Similar questions

Q. Find the value of

tan [\frac{π}{4} + \frac{1}{2} {cos}^{- 1} \frac{a}{b}] + tan ⌊ \frac{π}{4} - \frac{1}{2} {cos}^{- 1} \frac{a}{b} ⌋

Q. If

{tan}^{- 1} (- x) + {cos}^{- 1} (\frac{- 1}{2}) = \frac{π}{2}

, them the value of

x

Inverse circular functions,Principal values of

{s i n}^{- 1} x, {c o s}^{- 1} x, {t a n}^{- 1} x

{t a n}^{- 1} x + {t a n}^{- 1} y = {t a n}^{- 1} \frac{x + y}{1 - x y}

x y < 1

π + {t a n}^{- 1} \frac{x + y}{1 - x y}

x y > 1

Evaluate

(a)

{c o s}^{- 1} x + {c o s}^{- 1} [\frac{x}{2} + \frac{\sqrt{(3 - 3 x^{2})}}{2}]

(\frac{1}{2} \leq x \leq 1)

(b)

c o s (2 {c o s}^{- 1} x + {s i n}^{- 1} x)

x = 1 / 5

where

0 \leq {c o s}^{- 1} x \leq π

and

- π / 2 \leq {s i n}^{- 1} x \leq π / 2

Q. Inverse circular functions,Principal values of

{s i n}^{- 1} x, {c o s}^{- 1} x, {t a n}^{- 1} x

{t a n}^{- 1} x + {t a n}^{- 1} y = {t a n}^{- 1} \frac{x + y}{1 - x y}

x y < 1

π + {t a n}^{- 1} \frac{x + y}{1 - x y}

x y > 1

.
Prove that
(a)

2 {t a n}^{- 1} \frac{1}{5} + {s e c}^{- 1} \frac{5 \sqrt{2}}{7} + 2 {t a n}^{- 1} \frac{1}{8} = \frac{π}{4}

(b)

{c o s}^{- 1} \frac{12}{13} + 2 {c o s}^{- 1} \sqrt{(\frac{64}{65})} + {c o s}^{- 1} \sqrt{(\frac{49}{50})} = {c o s}^{- 1} \frac{1}{\sqrt{2}}

The value of $c o s [2 t a n^{- 1} (7)]$ is

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The value of tan[cos−1(−27)−π2] is

The correct option is A 23√5 tan[cos−1(−27)−π2]=tan[π−cos−1(27)−π2]=tan[π2−cos−1(27)]=cot(cos−1(27))=cot(cot−1(2√45))=2√45=23√5

The value of $t a n [c o s^{- 1} (\frac{- 2}{7}) - \frac{π}{2}]$ is