Question

secD=5/4. Evaluate

1-tanD/1+tanD

Answer 1

ANSWER

• The value of the above expression is 1/7

GIVEN:

• Sec D = 5/4

TO FIND:

$\frac{1 - \tan \: d}{1 + \tan \: d}$

SOLUTION:

Formula

$1 + \tan {}^{2} d \: = \sec {}^{2} d$

Putting Sec d = 5/4

$\implies \: \tan {}^{2} d \: = \sec {}^{2} d - 1 \\ \implies \: \tan {}^{2} d = (\frac{5}{4}) { }^{2} - 1 \\ \implies \: \tan {}^{2} d \: = \frac{25}{16} - 1 \\ \implies \: \tan {}^{2} d \: = \frac{9}{16} \\ \implies \: \tan d \: = \sqrt{ \frac{9}{16} } \\ \implies \: \tan d = \frac{3}{4}$

Putting tan d = 3/4

$= \frac{1 - \tan \: d}{1 + \tan \: d} \\ = \frac{1 - \frac{3}{4} }{1 + \frac{3}{4} } \\ = \frac{ \frac{1}{4} }{ \frac{7}{4} } \\ = \frac{1}{4} \times \frac{4}{7} \\ = \frac{1}{7}$

So , the value of the above expression is 1/7

SOME IMPORTANT FORMULA

Tan A = perpendicular/ base

Sin A = perpendicular/ hypotenuse

Cos A = Base / hypotenuse