Math, asked by manyaaa8589, 7 months ago

If tanA =m /m-1 and tanB =1 /2m-1 then prove that A-B =45 °

Answers

Answered by shwetharani537
3

Answer:

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Answered by Anonymous
2

 \huge\mathfrak\purple{Answer:}

We know that....

tan(A-B)= \frac{tanA-tanB}{1+tanAtanB}

Putting the values of tanA and tanB in

 \frac{tanA-tanB}{1+tanAtanB}

=>tan(A-B)= </strong><strong> \</strong><strong>huge</strong><strong>\</strong><strong>tt</strong><strong>\</strong><strong>frac</strong><strong>{</strong><strong> \</strong><strong>frac</strong><strong>{</strong><strong>m</strong><strong>}</strong><strong>{</strong><strong>m-1</strong><strong>}</strong><strong>-</strong><strong> \</strong><strong>frac</strong><strong>{</strong><strong>1</strong><strong>}</strong><strong>{</strong><strong>2m-1</strong><strong>}</strong><strong>}{</strong><strong>1</strong><strong>+</strong><strong> </strong><strong>\frac{m}{m-1}</strong><strong> </strong><strong>x</strong><strong> </strong><strong>\frac{</strong><strong>1</strong><strong>}{</strong><strong>2m-1</strong><strong>}</strong><strong>}

=>tan(A-B)=  \huge\tt\frac{ \frac{</strong><strong>2m</strong><strong>²</strong><strong>-</strong><strong>m-m</strong><strong>+</strong><strong>1</strong><strong>}{</strong><strong>2m²-</strong><strong>m-2</strong><strong>m+1</strong><strong>}</strong><strong>}</strong><strong>{</strong><strong>\frac{2m²-</strong><strong> \</strong><strong>cancel</strong><strong>{</strong><strong>m</strong><strong>}</strong><strong>-2</strong><strong>m+</strong><strong>1</strong><strong>+</strong><strong> \</strong><strong>cancel</strong><strong>{</strong><strong>m</strong><strong>}</strong><strong>}{2m²-m-2m+1}</strong><strong>}

=>tan(A-B)=  \huge\tt\frac{ \frac{2m²-m-m+1}{</strong><strong> \</strong><strong>sout</strong><strong>{</strong><strong>2m²-m-2m+</strong><strong>1</strong><strong>}</strong><strong>}}{\frac{2m²-2m+1}{</strong><strong> \</strong><strong>sout</strong><strong>{</strong><strong>2m²-m-2m+</strong><strong>1</strong><strong>}</strong><strong>}}

=>tan(A-B)=  \huge\tt\frac</strong><strong>{2m²-</strong><strong>2m</strong><strong>+1}{</strong><strong>2</strong><strong>m²-</strong><strong>2m</strong><strong>+</strong><strong>1</strong><strong>}

=>tan(A-B)=  \huge\tt\frac{</strong><strong> \</strong><strong>cancel</strong><strong>{</strong><strong>2m²-2m+</strong><strong>1</strong><strong>}</strong><strong>}{</strong><strong> \</strong><strong>cancel</strong><strong>{</strong><strong>2m²-2m+</strong><strong>1</strong><strong>}</strong><strong>}

=>tan(A-B)=  \huge\tt\frac{1}{1}

=>tan45°=1

Therfore A-B=45

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