Question

if tan theta = 3/4 find 1-cos^2 theta/1+cos^2. ​

Answer 1

Answer:

9/41

Explanation:

Trigonometric Ratio- Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

Solving way-

Given- $Tantheta=3/4$

By $Pythagoes theorem H=5$

Now apply this value in equation get 9/41

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Answer 2

Answer:

The ratios of the sides of a right-angled triangle to an acute angle are known as its trigonometric ratios.

Step-by-step explanation:

What is meant by Trigonometric Ratios?

As specified by the definition of a right-angled triangle's side ratio, trigonometric ratios are the values of all trigonometric functions. The trigonometric ratios of a certain acute angle are the ratios of a right-angled triangle's sides to that angle.

The usage of trigonometric ratios in a variety of fields—such as civil engineering, architecture, mechanical engineering, medical imaging, electronics, electrical engineering, chemistry, geography, computer music development, oceanography, seismology, and phonetics—makes them significant.

Given,

$& \tan \theta=\frac{3}{4}$

$& \Rightarrow \tan ^2 \theta=\frac{9}{16}$

$& \Rightarrow \sec ^2 \theta=1+\frac{9}{16}=\frac{25}{16}$

$\Rightarrow \cos ^2 \theta=\frac{16}{25}$

$& \Rightarrow \cos \theta=\frac{4}{5}$

Let the equation be $\frac{1-\cos^{2} \theta}{1+\cos^{2} \theta}$

$=\frac{1-\frac{4}{5}}{1+\frac{4}{5}} .$

(replacing value of $\cos \theta$ )

$=\frac{1}{9}$

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