Question

iif cosectheta-cottheta=1\2 then costheta=?

Answer 1

I'll use O for theta:-

csc O - cot O = 1/2 what is cos O

you might do it this way

csc^2 O = 1 + cot^2 O

so substituting ;

sqrt( 1 + cot^2 O) + cot O = 1/2

solve for cot O

then you can find cos O using other trig identities

Answer 2

* typo in line 6
it should be
sqrt( 1 + cot^2 O) - cot O = 1/2

Answer 3

you can also find the value of angle O from cot O
then find cos O

Answer 4

I'll start the solution of the equation for you
sqrt( 1 + cot^2 O) + cot O = 1/2
sqrt( 1 + cot^2 O) = cot O + 1/2
square both sides;-
1 + cot^2 O = cot^2 O + cot O + 1/4

now finding cot O is straightforward

Answer 5

\(csc \theta =\dfrac{1}{sin\theta}\\cot \theta=\dfrac{cos\theta}{sin\theta}\)

hence \(csc(\theta)-cot(\theta)= \dfrac{1}{sin(\theta)}-\dfrac{cos(\theta)}{sin(\theta)}=\dfrac{1-cos(\theta)}{sin(\theta)}=\dfrac{1}{2}\)

Answer 6

Now, restrict the solution from 0, since if \(\theta =0\) , then \(sin(\theta )=0\), that make the expression undefined.

Answer 7

we have: \(2(1-cos(\theta))= sin(\theta)\)
square both sides and solve for \(cos (\theta)\)