Question

3x=5y=(75)z find the relation among x,y,z
A=60° B=30 verify that tan(A-B)=tanA-tanB/1+tanAtanB

Answer 1

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• Verify the following.

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Given,

$\sf \alpha = 60 \degree$

$\sf \beta = 30 \degree$

Now,

$\sf \tan( \alpha - \beta ) = \tan(60 \degree - 30 \degree)$

$\sf = \tan 30 \degree$

$\sf = \frac{1}{ \sqrt{3} }$

Now,

$\sf\frac{ \tan \alpha - \tan \beta }{1 + \tan \alpha \tan \beta }$

$= \sf \frac{ \tan60 \degree - \tan30 \degree}{1 + \tan60 \degree \tan30 \degree }$

$\large\sf = \frac{ \sqrt{3} - \frac{1}{ \sqrt{3} } }{1 + ( \cancel{\sqrt{3}} \times \frac{1}{ \cancel{\sqrt{3} }} ) }$

$\large\sf = \frac{ \frac{3 - 1}{ \sqrt{3} } }{1 + 1}$

$\sf = \frac{ \cancel{2}}{ \sqrt{3} } \times \frac{1}{ \cancel{2} }$

$\sf = \frac{1}{ \sqrt{3} }$

Therefore,

$\boxed{ \sf \tan( \alpha - \beta ) = \frac{ \tan \alpha - \tan \beta }{1 + \tan \alpha \tan \beta } }$

Hence, Verified.

Answer 2

Answer:

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