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If c o s θ = x x + 1 , then θ is:

(a)   An acute angle

(b)   A right angle

(c)   An obtuse angle

(d)   Not possible

0 2 Views | Posted 3 months ago
Asked by Shiksha User

  • 1 Answer

  • A

    Answered by

    alok kumar singh | Contributor-Level 10

    3 months ago

    This is an Objective Type Questions as classified in NCERT Exemplar

    Sol:

    G i v e n     t h a t : c o s θ = x + 1 x                 ⇒ c o s θ = x 2 + 1 x ⇒                                         x 2 + 1 = x c o s θ             ⇒ x 2 − x c o s θ + 1 = 0 F o r     r e a l     v a l u e     o f     x ,     b 2 − 4 a c ≥ 0 ⇒                                         ( − c o s θ ) 2 − 4 × 1 × 1 ≥ 0 ⇒                                                                               c o s 2 θ − 4 ≥ 0             ⇒ c o s 2 θ ≥ 4 ⇒                                                                                                   c o s θ ≥ ± 2                                                           [ − 1 ≤ c o s θ ≤ 1 ] S o ,     t h e     v a l u e     o f     θ     i s     n o t     p o s s i b l e . H e n c e ,     t h e     c o r r e c t     o p t i o n     i s     ( d ) .

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