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  1. If
    tan θ + cot θ
    = 2, (0 ≤ θ ≤ 90°),then the value of sin θ is
    tan θ - cot θ
    1. 2
      3
    2. 3
      2
    3. 1
      2
    4. 1
Correct Option: B

tan θ + cot θ
=
2
tan θ - cot θ1

By componendo and dividendo,
2 tan θ
=
3
2 cot θ1

sin θ
.
sin θ
= 3
cos θcos θ

&rArr sin² θ = 3cos² θ
&rArr sin² θ = 3 (1 – sin² θ)
&rArr 4 sin² θ = 3
⇒ sin² θ =
3
4

⇒ sin θ =
3
2



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