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Values of Trigonometric Ratios

If x=cos-1c...

Question

If $x = {cos}^{- 1} (cos 4) : y = {sin}^{- 1} (sin 3)$ then which of the following holds?

A

x - y = 1

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B

x + y + 1 = 0

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C

x + 2 y = 2

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D

tan (x + y) = - tan 7

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Solution

The correct option is D $tan (x + y) = - tan 7$
Given, $x = {cos}^{- 1} (cos 4)$
$= 2 π - 4$
and $y = {sin}^{- 1} (sin 3)$
$= π - 3$
$tan (x + y)$
$= tan (3 π - 4 - 3)$
$= tan (3 π - 7)$
$= - tan (7)$

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