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JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

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Application +4 | -1

If

\cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=3 \pi

then

x y+y z+z x

is equal to :

View answer and explanation

Correct option: D

3

Option D is correct because when

\cos^{-1}x + \cos^{-1}y + \cos^{-1}z = 3\pi

, it implies

x=y=z=-1

, and therefore

xy+yz+zx = 3

.

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\cos ^ {-1}\left\{\frac{1}{\sqrt{2}}\left(\cos \frac{9 \pi}{10}-\sin \frac{9 \pi}{10}\right)\right\}=

\sin \left(\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right)=1

x

{x^2} + {y^2} + {z^2} = {r^2},

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2{\tan ^{ - 1}}\left( {\frac{1}{3}} \right) + {\tan ^{ - 1}}\left( {\frac{1}{7}} \right)