The value of tan - 1 cos 15 π 4 - 1 sin π 4 is equal to

Given, tan - 1 cos 15 π 4 - 1 sin π 4 = tan - 1 cos 4 π - π 4 - 1 sin π 4 = tan - 1 1 2 - 1 1 2 = tan - 1 1 - 2 = - tan - 1 2 - 1 = - π 8

Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

MathematicsInverse Trigonometric FunctionsGeneral ( General, Domain, Range & Graph)Easy2 minPYQ_2022

MathematicsEasysingle choice

The value of $\tan^{- 1} [\frac{\cos (\frac{15 π}{4}) - 1}{\sin (\frac{π}{4})}]$ is equal to

Answer:

Solution:

Given,

$\tan^{- 1} (\frac{\cos (\frac{15 π}{4}) - 1}{\sin \frac{π}{4}})$

$= \tan^{- 1} (\frac{\cos (4 π - \frac{π}{4}) - 1}{\sin \frac{π}{4}})$

$= \tan^{- 1} (\frac{\frac{1}{\sqrt{2}} - 1}{\frac{1}{\sqrt{2}}})$

$= \tan^{- 1} (1 - \sqrt{2}) = - \tan^{- 1} (\sqrt{2} - 1)$

$= - \frac{π}{8}$

Stream:JEESubject:MathematicsTopic:Inverse Trigonometric FunctionsSubtopic:General ( General, Domain, Range & Graph)

⏱ 2mℹ️ Source: PYQ_2022

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