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Prove that Sin25 degree+cos25 degree/sin25 degree-cos25 degree=tan110 degree

Prove that Sin25 degree+cos25 degree/sin25 degree-cos25 degree=tan110 degree

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2 Answers

Susmita
425 Points
5 years ago
Divide numerator and denominator by cos25°.
\frac{tan25° +1}{tan25° -1}
=\frac{-(tan25° +1)}{1-tan25°}
=\frac{-(tan25° +tan45)}{1-tan25°tan45} 
=-tan(25+45)=-tan70=tan(180-70)=tan110
In the 3rd line we have replaced 1 by tan45.In the 4th line we have incorporated tan(A+B) formula.
Please approve the answer if you are helped.
Samyog Sapkota
15 Points
3 years ago
First Dividing numerator and denominator by cos25 .
= 1 + TAN 25 / 1-TAN25
= TAN 45 + TAN 25 / 1- TAN 45 TAN 25 
= TAN ( 45 + 25 ) 
TAN 70 
HOPE YOU UNDERSTOOD

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