If $tan(α+β) = a$, $tan(&alph

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Home Questions XVBU6WSC9Q

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

If $tan(α+β) = a$, $tan(α-β) = b$, then the value of $tan2α$ is :

Options:

$\frac{a+b}{1-ab}$

$\frac{a+b}{1+ab}$

$\frac{a-b}{1+ab}$

$\frac{a-b}{1-ab}$

Correct Answer:

$\frac{a+b}{1-ab}$

Explanation:

2α = ( α + β ) + ( α - β )

tan2α = tan [ ( α + β ) + ( α - β ) ]

= $\frac{tan( α + β ) + tan ( α - β ) }{ 1 - tan( α + β ) . tan ( α - β )}$

Put putting values of tan( α + β ) = a & tan( α - β ) = b

= $\frac{a+ b }{ 1 - a . b}$