Question

if tan theta = 20/21 then find value of other trigonomertic ratio ​

Answer 1

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1+sinθ+cosθ1−sinθ+cosθ is 73 .

To find:

Evaluate \frac{1-\sin \theta+\cos \theta}{1+\sin \theta+\cos \theta}1+sinθ+cosθ1−sinθ+cosθ

Solution:

Given: \tan \theta=\frac{20}{21}tanθ=2120

The hypotenuse will be 29 by Pythagoras theorem.

Then \sin \theta=\frac{20}{29}\ \&\ \cos \theta=\frac{21}{29}sinθ=2920 & cosθ=2921

\frac{1-\sin \theta+\cos \theta}{1+\sin \theta+\cos \theta}1+sinθ+cosθ1−sinθ+cosθ

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]}[1+(2920)+(2921)][1−(2920)+(2921)]

=\frac{\left[29-\frac{20}{29}+\frac{21}{29}\right]}{\left[29+\frac{20}{29}+\frac{21}{29}\right]}=[29+2920+2921][29−2920+2921]

=\frac{29-20+21}{29+20+21}=29+20+2129−20+21

=\frac{30}{70}=7030

=\frac{3}{7}=73

“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’.

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Answer 2

This is the answer of the question