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NCERT Class XI Mathematics - Trigonometric Functions - Solutions

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Question : 24
Total: 61
tan(
π
4
+x)
tan(
π
4
−x)
 = (
1+tanx
1−tanx
)2
Solution:  
We have, L.H.S. =
tan(
π
4
+x)
tan(
π
4
−x)
 =
tan
π
4
+tanx
1−tan
π
4
.tanx
tan
π
4
−tanx
1+tan
π
4
.tanx
Since tan (A + B) =
tanA+tanB
1−tanAtanB
 and tan (A - B) =
tanA−tanB
1+tanAtanB
=
1+tanx
1−tanx
1−tanx
1+tanx
 =
1+tanx
1−tanx
 ×
1+tanx
1−tanx
 = (
1+tanx
1−tanx
)2 = R.H.S.
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