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Question
State whether the statement is True or False? Also give justification.
If tanA = `(1 - cos B)/sinB`, then tan2A = tanB
Options
True
False
Solution
This statement is True.
Explanation:
Given that: tanA = `(1 - cosB)/sinB`
= `(2sin^2 B/2)/(2sin B/2 cos B/2)`
= `tan B/2`
tan2A = `(2tanA)/(1 - tan^2 A)`
= `(2tan B/2)/(1 - tan^2 B/2)`
∴ tan2A = tanB
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