tan 2theta=2tan theta/1-tansquare theta. if theta=30
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Answer:
Answer
Given θ=30
∘
To verify,
(i) tan2θ=
1−tan
2
θ
2tanθ
tan2(30
∘
)=
1−tan
2
30
∘
2tan30
∘
tan(60
∘
)=
1−tan
2
30
∘
2tan30
∘
3
=
1−(
3
1
)
2
2×
3
1
3
=
1−(
3
1
)
3
2
3
=
3
2
3
2
3
=
3
(ii) tan2θ=
1+tan
2
θ
4tanθ
We have, 1+tan
2
θ=sec
2
θ
∴tan2θ=
sec
2
θ
4tanθ
tan2(30
∘
)=
sec
2
30
∘
4tan30
∘
tan(60
∘
)=
sec
2
30
∘
4tan30
∘
3
=
(
3
2
)
2
4
3
1
3
=
3
4
3
4
3
=
3
3
3
=
3
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