Question

If tan theta =20/21 , evaluate 1-sin theta +cos theta /1 +sin theta +cos theta.

Answer 1

tanθ = 20/21
so, sinθ =20/29
cosθ = 21/29

now,
(1-sinθ+cosθ)/(1+sinθ + cosθ)

putting the values,

[1 - (20/29)+(21/29)]/[1 +(20/29)+(21/29)]
=(29-20+21)/(29+20+21)
=30/70
=3/7

Answer 2

$\frac{1-\sin \theta+\cos \theta}{1+\sin \theta+\cos \theta}\ is\ \bold{\frac{3}{7}}$.

To find:

Evaluate $\frac{1-\sin \theta+\cos \theta}{1+\sin \theta+\cos \theta}$

Solution:

Given: $\tan \theta=\frac{20}{21}$

The hypotenuse will be 29 by Pythagoras theorem.

Then $\sin \theta=\frac{20}{29}\ \&\ \cos \theta=\frac{21}{29}$

$\frac{1-\sin \theta+\cos \theta}{1+\sin \theta+\cos \theta}$

Replacing the values with above, we have

$\frac{\left[1-\left(\frac{20}{29}\right)+\left(\frac{21}{29}\right)\right]}{\left[1+\left(\frac{20}{29}\right)+\left(\frac{21}{29}\right)\right]}$

$=\frac{\left[29-\frac{20}{29}+\frac{21}{29}\right]}{\left[29+\frac{20}{29}+\frac{21}{29}\right]}$

$=\frac{29-20+21}{29+20+21}$

$=\frac{30}{70}$

$=\frac{3}{7}$

“Sine, cosine and tangent” are main functions in trigonometry. We are mainly derived this functions using formulas. ‘Trigonometric functions’ have been ‘extended as functions’ of a “real or complex variable”, which are today ‘pervasive in all mathematics’.