Home » Aptitude » Trigonometry » Question
  1. The value of  
    sinθ + sinφ
    +
    cosθ − cosφ
      is :
    cosθ + cosφsinθ − sinφ
    1. 1
    2. 2
    3. 1/2
    4. 0
Correct Option: D

Expression =
sinθ + sinφ
+
cosθ - cosφ
cosθ + cosφsinθ - sinφ

=
(sinθ + sinφ)(sinθ - sinφ) + (cosθ - cosφ)(cosθ + cosφ)
(cosθ + cosφ)(sinθ - sinφ)

=
sin²θ + sin²φ + cos²θ - cos²φ
(cosθ + cosφ)(sinθ - sinφ)

=
(sin²θ + cos²θ) - (sinφθ + cos²φ)
(cosθ + cosφ)(sinθ - sinφ)

=
1 - 1
= 0
(cosθ + cosφ)(sinθ - sinφ)



Your comments will be displayed only after manual approval.