If x -sin -1sin 10 and y -cos -1cos 10- then y - x is equal to-A- 0B- 10C- 7 -D- -

The correct option is D πx = sin^ 1(sin10) ⇒ x = sin^ 1 (sin(3π 10)) ⇒ x = 3π 10 Now, y = cos^ 1(cos (10) ) ⇒ y = cos^ 1(cos(4π 10) ) ⇒ y = 4π 10 ∴ ...

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Byju's Answer

Standard XII

Mathematics

Composition of Inverse Trigonometric Functions and Trigonometric Functions

If x =sin -1s...

Question

If $x = {sin}^{- 1} (sin 10)$ and $y = {cos}^{- 1} (cos 10)$ , then $y - x$ is equal to :

0

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π

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10

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7 π

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Solution

The correct option is B $π$
$x = {sin}^{- 1} (sin 10)$
$\Rightarrow x = {sin}^{- 1} (sin (3 π - 10))$
$\Rightarrow x = 3 π - 10$

Now, $y = {cos}^{- 1} (cos (10))$
$\Rightarrow y = {cos}^{- 1} (cos (4 π - 10))$
$\Rightarrow y = 4 π - 10$
$∴ y - x = 4 π - 10 - 3 π + 10$
$\Rightarrow y - x = π$

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If x=sin−1(sin10) and y=cos−1(cos10), then y−x is equal to :

The correct option is B πx=sin−1(sin10) ⇒ x=sin−1(sin(3π−10)) ⇒ x=3π−10 Now, y=cos−1(cos(10)) ⇒ y=cos−1(cos(4π−10)) ⇒ y=4π−10 ∴ y−x=4π−10−3π+10 ⇒ y−x=π

If $x = {sin}^{- 1} (sin 10)$ and $y = {cos}^{- 1} (cos 10)$ , then $y - x$ is equal to :