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Find the most general value of θ satisfying the equation tanθ=−1  and  cosθ=12.  

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 a Short Answer Type Questions as classified in NCERT Exemplar

    Sol:

    G i v e n     t h a t : t a n θ = − 1     a n d     c o s θ = 1 2                                                     t a n θ = − 1 ⇒                                           t a n θ = t a n ( − π 4 ) ⇒                                           t a n θ = t a n ( 2 π − π 4 )         ⇒ t a n θ = t a n 7 π 4 ∴                                                             θ = 7 π 4 N o w ,                             c o s θ = 1 2           ⇒ c o s θ = c o s π 4 ⇒                                           c o s θ = c o s ( 2 π − π 4 ) ⇒                                           c o s θ = c o s 7 π 4 ∴                                                               θ = 7 π 4                                 [ t a n θ     a n d     c o s θ     a r e     p o s i t i v e     i n     4 t h     q u a d r a n t ] H e n c e ,     t h e     m o s t     g e n e r a l     v a l u e     o f     θ     a r e     2 n π + 7 π 2 .

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