Question

find the value of cos 20 - sin 20 by cos 20 + sin 20​

Answer 1

Answer:

$\frac{cos\:20-sin\:20}{cos\:20+sin\:20}=tan\:25$

Step-by-step explanation:

Formula used:

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

$Now,\\\\\frac{cos\:20-sin\:20}{cos\:20+sin\:20}\\\\\\take\:cos\;20\: common\:from\:both\:numerator\:and\:denominator\\\\=\frac{cos\:20}{cos\:20}[\frac{1-\frac{sin\:20}{cos\:20}}{1+\frac{sin\:20}{cos\:20}}]\\\\=\frac{1-tan\;20}{1+tan\:20}\\\\=\frac{tan\:45-tan\;20}{1+1.tan\:20}\\\\=\frac{tan\:45-tan\;20}{1+tan45.tan\:20}\\\\=tan(45-20)\\\\=tan\:25$

Answer 2

Answer: The answer is tan25

Step-by-step explanation:

Given,  Cos20-sin20/cos20+sin20

First we take cos 20 common from numerator and denominator

cos20(1-sin20/cos20)/cos20(1+sin20/cos20)

then cos20 and cos 20 cancelled form numerator and denominator and we get,

sin20/cos20=tan20

now remaining part is

1-tan20/1+tan20 eq 1

1 can be rewritten as 1=tan 45 eq2

by eq 1 and eq 2, we get

=tan45-tan20/1-tan45.tan20 eq 3

Since,  tan(A-B)=tanA-tanB/1-tanA.tanB eq 4

So, we get

tan45-tan20/1-tan45.tan20

=tan (45-20)

= tan25

Hope it helps!

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