Question

if tan theta= 15/7 find cos theta + sin theta/ cos theta- sin theta
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Answer 1

$Given \:tan \theta = \frac{15}{7} \: ---(1)$

$\red{Value \: of \: \frac{cos \theta + sin \theta}{cos \theta - sin \theta }}$

$Dividing \:numerator\:and \:denominator\: by \\ \blue {cos \theta } \:we \: get$

$= \frac{ 1 + tan \theta }{1 - tan \theta } \\= \frac{ 1 + \frac{15}{7}}{ 1 - \frac{15}{7}} \\= \frac{ \frac{7+15}{7}}{\frac{7-15}{7}}\\= \frac{22}{-8} \\= \frac{-11}{4}$

Therefore.,

$\red{Value \: of \: \frac{cos \theta + sin \theta}{cos \theta - sin \theta }}\green { = \frac{-11}{4} }$

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Answer 2

tan theta=P/B=15/7

this implies P=15 and B=7

H^2= P^2+B^2

=225+49

=274H = √ 274 = 16.55

Now, cos theta+ sin theta/cos theta-sin theta

= B/H + P/H ÷ B/H - P/H

= 7/16.55 + 15/16.55 ÷ 7/16.55 - 15/16.55 = 22/16.55 ÷ -8/16.55 =22/16.55×16.55/-8

=22/-8

= -11/4

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