Please solve correctly

fomenos

Answer:

Step-by-step explanation:

$\large\underline{\sf{Solution-}}$

<h2 /><h2><u>Consider</u></h2>

$\rm \: \cos \bigg( \dfrac{3\pi}{2} + x \bigg) \cos \: (2\pi + x) \bigg \{ \cot \bigg( \dfrac{3\pi}{2} - x \bigg) + cot(2\pi + x) \bigg \}cos(23π+x)cos(2π+x)$

$\rm \: \cos \bigg( \dfrac{3\pi}{2} + x \bigg) = sinx$

$\rm \: {cos \: (2\pi + x) }$

$\rm \: \cot \bigg( \dfrac{3\pi}{2} - x \bigg) \: = \: tanx$

$\rm \: cot(2\pi + x) \: = \: cotx$

So, on substituting all these values, we get

$\rm \: = \: sinx \: cosx \: (tanx \: + \: cotx)$

$\rm \: = \: sinx \: cosx \: \bigg(\dfrac{sinx}{cosx} + \dfrac{cosx}{sinx}$

$\rm \: = \: sinx \: cosx \: \bigg(\dfrac{ {sin}^{2}x + {cos}^{2}x}{cosx \: sinx}$

$\rm \: = \: 1=1$

<h2>Hence,</h2>

$\boxed{\tt{ \cos \bigg( \frac{3\pi}{2} + x \bigg) \cos \: (2\pi + x) \bigg \{ \cot \bigg( \frac{3\pi}{2} - x \bigg) + cot(2\pi + x) \bigg \} = 1}}$

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<h2>ADDITIONAL INFORMATION :-</h2>

Sign of Trigonometric ratios in Quadrants

sin (90°-θ) = cos θ
cos (90°-θ) = sin θ
tan (90°-θ) = cot θ
csc (90°-θ) = sec θ
sec (90°-θ) = csc θ
cot (90°-θ) = tan θ
sin (90°+θ) = cos θ
cos (90°+θ) = -sin θ
tan (90°+θ) = -cot θ
csc (90°+θ) = sec θ
sec (90°+θ) = -csc θ
cot (90°+θ) = -tan θ
sin (180°-θ) = sin θ
cos (180°-θ) = -cos θ
tan (180°-θ) = -tan θ
csc (180°-θ) = csc θ
sec (180°-θ) = -sec θ
cot (180°-θ) = -cot θ
sin (180°+θ) = -sin θ
cos (180°+θ) = -cos θ
tan (180°+θ) = tan θ
csc (180°+θ) = -csc θ
sec (180°+θ) = -sec θ
cot (180°+θ) = cot θ
sin (270°-θ) = -cos θ
cos (270°-θ) = -sin θ
tan (270°-θ) = cot θ
csc (270°-θ) = -sec θ
sec (270°-θ) = -csc θ
cot (270°-θ) = tan θ
sin (270°+θ) = -cos θ
cos (270°+θ) = sin θ
tan (270°+θ) = -cot θ
csc (270°+θ) = -sec θ
sec (270°+θ) = cos θ
cot (270°+θ) = -tan θ

7 0

2 years ago

Read 2 more answers

Which inequality is graphed below

Aneli [31]

Answer:

C.

Step-by-step explanation:

> is a dotted line and the area above it is shaded

< is a dotted line and the area below it is shades

≥ is solid line with the area above shaded

≤ is a solid line with the area below it shaded

The graph shows characteristics of ≥, and C is the only answer with ≥ in it

6 0

3 years ago

Alexandria purchased a computer on sale. The original price was $1200. The sale price was 5/6 of the original price. how much di

Vaselesa [24]

I believe you ment to say sale price but I hope this helps you understand your question. The original price was 1200, and if it were 5/6 on sale (this method works for all questions like this) you would do 1200 ÷ 6 = 200 x 5 = $1000.

7 0

3 years ago

Thomas runs 34 of a mileevery day for 5 days. Howfar has he run total?

STALIN [3.7K]

Guven:

Miles per day = 34 miles

Number of days = 5 days

To find the total distance(miles), we have:

Total distance = distance covered per day x Number per days

= 34 x 5 = 170 miles

Therefore, the total distance he has covered is 170 miles

ANSWER:

170 miles

4 0

1 year ago

What is the length of the tabletop

zzz [600]

The table's length is 186 centimeters..........................

5 0

3 years ago