Question

If tan theta =20/21 show that 1-sin theta +cos theta / 1+sin theta+cos theta =3/7
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Answer 1

Answer:

tanø=20/21

i.e.; tan ø= p/b

I.e.; p=20x , b=21x.........(let)

Now , By pythagorean theorem , we get,

h²=(20x)²+(21x)²

= 400x²+441x²

=841x²

${h}^{2} = \sqrt{841 {x}^{2} } = 29$

sinø= 20/29

cosø=21/29

$\frac{1 - \sin(ø) + \cos(ø) }{1 + \sin(ø) + \ \cos(ø) } \\ = \frac{1 - \binom{20}{29} + \binom{21}{29} }{1 + \binom{20}{29} + \binom{21}{29}} \\ = \frac{29 - 20 + 21}{29 - 20 + 21} \\ = \frac{50 - 20}{50 + 20} \\ \frac{30}{70} \\ \frac{3}{7}$

Hence verified.

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Answer 2

I HOPE IT HELPFUL ANSWER.