Question

If sin A = 4/5 then the value of 1-cos a /1+cos a
a) 1/8
b) 1/2
c)2
d)3/5

Answer 1

Step-by-step explanation:

Given (1+cosA)(1−cosA)=43

⟹1−cos2A=43

⟹cos2A=1−43

⟹cos2A=44−3

⟹cos2A=41

⟹sec2A=4

⟹secA=±2

Answer 2

Given:

SinA = 4/5.

To Find:

value of (1-cosA)/(1+cosA).

Solution:

The given question can be solved by using the concepts of trigonometry.

1. It is given that the value of SinA is 4/5.

• According to the properties of trigonometry, In a right-angled triangle, the sine of an angle is formulated as (length of the opposite side)/(length of the hypotenuse).
• cosine of an angle is formulated as (length of the adjacent side)/(length of the hypotenuse)

2. SinA = 4/5,

=> (length of opposite side/length of hypotenuse) = (4/5)

=> lenght of adjacent side can be found using pythogoras theorem,

• hypotenuse = $\sqrt{(opposite side length)^{2}+(adjacent side length)^{2} }$,

=> 25 = 16 + $(adjacentside)^{2}$,

=> $\sqrt{25-16}$ = length of adjacent side,

=> lenght of adjacent side = 3.

• Hence, the value of CosA is 3/5.

3. Substitute the value of CosA in the given expression,

=>$\frac{1-CosA}{1+ CosA}$,

=>$\frac{2/5}{8/5}$,

=>$\frac{2}{8}$,

=> 1/4.  

Therefore, the value of the expression$\frac{1-CosA}{1+CosA}$ is 1/4.