If tanθ+cotθ=2, then find the value of tan
53
θ+cot
38
θ.
- A-1
- B0
- C2
- D1
Solution & Step-by-step Explanation
Given equation:
tanθ+cotθ=2
Since cotθ=
tanθ
1
, we can rewrite it as:
tanθ+
tanθ
1
=2
tan
2
θ+1=2tanθ
tan
2
θ−2tanθ+1=0
(tanθ−1)
2
=0⟹tanθ=1
Since tanθ=1, then cotθ=
1
1
=1.
Now, substitute these values into the required expression:
tan
53
θ+cot
38
θ=(1)
53
+(1)
38
=1+1=2
tanθ+cotθ=2
Since cotθ=
tanθ
1
, we can rewrite it as:
tanθ+
tanθ
1
=2
tan
2
θ+1=2tanθ
tan
2
θ−2tanθ+1=0
(tanθ−1)
2
=0⟹tanθ=1
Since tanθ=1, then cotθ=
1
1
=1.
Now, substitute these values into the required expression:
tan
53
θ+cot
38
θ=(1)
53
+(1)
38
=1+1=2