If c o s − 1 x + c o s − 1 y + c o s − 1 z = 3 π , then x y + y z + z x = Options: A . &nbsp 0 B . &nbsp 1 C . &nbsp 3 D . &nbsp -3

Answer: Option C : C Given c o s − 1 x + c o s − 1 y + c o s − 1 z = 3 π ∵ 0 ≤ c o s − 1 x ≤ π ∴ 0 ≤ c o s − 1 y ≤ π and 0 ≤ c o s − 1 z ≤ π Here c o s − 1 x = c o s − 1 y = c o s − 1 z = π ⇒ x = y = z = c o s π = − 1 ∴ x y + y z + z x = ( − 1 ) ( − 1 ) + ( − 1 ) ( − 1 ) + ( − 1 ) ( − 1 ) = 1 + 1 + 1 = 3 .

If cos−1x+cos−1y+cos−1z=3π, then xy+yz+zx=

Discussion Forum : Inverse Trigonometric Functions

Question -

If $c o s^{- 1} x + c o s^{- 1} y + c o s^{- 1} z = 3 π$ , then $x y + y z + z x =$

Options:

A . 0

B . 1

C . 3

D . -3

Answer: Option C
:
C
Given

c o s^{- 1} x + c o s^{- 1} y + c o s^{- 1} z = 3 π

∵ 0 \leq c o s^{- 1} x \leq π

∴ 0 \leq c o s^{- 1} y \leq π

and

0 \leq c o s^{- 1} z \leq π

Here

c o s^{- 1} x = c o s^{- 1} y = c o s^{- 1} z = π

\Rightarrow x = y = z = c o s π = - 1

∴ x y + y z + z x = (- 1) (- 1) + (- 1) (- 1) + (- 1) (- 1)

= 1 + 1 + 1 = 3

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Discussion Forum : Inverse Trigonometric Functions

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