3csc^2(2x) + 2 cosec 2x = 1-cot^2(2x)

I am assuming you want to solve for x:-

Now cosec^2 2x = 1 - cot^2 2x  so the equation becomes

3 cosec^2(2x) + 2 cosec 2x =  cosec^2 2x

2 cosec^2 2x + 2 cosec 2x = 0

2 cosec 2x (  cosec 2x + 1) = 0

so 2 cosec 2x = 0  or    cosec 2x = -1

cosec 2x = 0  or cosec 2x = -1

cosec 2x = 0  is indeterminate so we ignore the first one

cosec 2x = -1  can be written as 1 / sin 2x = -1

so sin 2x = -1  

giving 2x = 270 degrees

Therefore  x = 135 degrees  answer

it is b)

hope this : )

step-by-step explanation:

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°