Mathematics, 15.10.2020 07:01, michael1498

Help please! I need to prove this using identities
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cos(pi/2+x)/cos(pi+x)=tanx

Answers: 2

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Answers

answered: dreamn6651

see proof below

Step-by-step explanation:

Use the Sum & Difference Identity: cos (A + B) = cos A · cos B - sin A · sin B

Recall the following from Unit Circle: cos (π/2) = 0, sin (π/2) = 1

cos (π) = -1, sin (π) = 0

Use the Quotient Identity: $\tan A=\dfrac{\sin A}{\cos A}$

Proof LHS → RHS:

$\text{LHS:}\qquad \qquad \dfrac{\cos \bigg(\dfrac{\pi}{2}+x\bigg)}{\cos \bigg(\pi +x\bigg)}$

$\text{Sum Difference:}\qquad \dfrac{\cos \dfrac{\pi}{2}\cdot \cos x-\sin \dfrac{\pi}{2}\cdot \sin x}{\cos \pi \cdot \cos x-\sin \pi \cdot \sin x}$

$\text{Unit Circle:}\qquad \qquad \dfrac{0\cdot \cos x-1\cdot \sin x}{-1\cdot \cos x-0\cdot \sin x}$

$=\dfrac{-\sin x}{-\cos x}$

Quotient: tan x

LHS = RHS $\checkmark$

Help please!

I need to prove this using identities show all stepscos(pi/2+x)/cos(pi+x)=tanx

answered: Guest

0.85 or 85%

step-by-step explanation:

1) divide 23 by 27

2) round the decimal to the nearest 10

3) so your answer would be 0.85 or 85%

answered: Guest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

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Help please! I need to prove this using identities
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cos(pi/2+x)/cos(...