Question

if tan theta 3 by 4 find the value of (1 - cos square theta by 1 + cos square theta)
​

Answer 1

Answer:

Answer: As we know. Cos theta = 1/sec theta. Now,. Sec^2 theta = 1+tan ^2 theta Now,. = 1+(3/4)^2 cos theta = 4/5.

15 votes

Answer 2

The value of given expression is  $\dfrac{9}{41}$ .

Given :

$tan \ \theta =\dfrac{3}{4}$

We need to find the value of :

$\dfrac{1-cos^2\ \theta}{1+cos^2\ \theta}$         .........( 1 )

We know ,

$sec^2\ \theta-tan^2\ \theta=1\\sec^2\ \theta- \dfrac{3^2}{4^2}=1\\\\sec\ \theta=\dfrac{5}{4}$

Also ,

$cos\ \theta=\dfrac{1}{sec\ \theta}\\\\cos\ \theta=\dfrac{4}{5}$

Putting the value of $cos\ \theta$ in equation 1 .

We get ,

$\dfrac{1-\dfrac{4^2}{5^2}}{1+\dfrac{4^2}{5^2}}\\\\\dfrac{9}{41}$

Hence , this is the required solution .

Learn More :

Trigonometry

https://brainly.in/question/4349306