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2 years ago

Cos x cos (-x) -sin x sin (-x) = 1. Verify the Identity. Please Show All Steps.

Mathematics

1 answer:

umka21 [38]2 years ago

8 0

Answer:

cos x cos (-x) -sin x sin (-x) = 1 ⇒ proved down

Step-by-step explanation:

* Lets revise the angles in the four quadrants

- If angle x is in the first quadrant, then the equivalent angles to it are

# 180 - x ⇒ second quadrant (sin (180 - x) = sin x , cos (180 - x) = -cos x

tan (180 - x) = -tan x)

# 180 + x ⇒ third quadrant (sin (180 - x) = -sin x , cos (180 - x) = -cos x

tan (180 - x) = tan x)

# 360 - x ⇒ fourth quadrant (sin (180 - x) = -sin x , cos (180 - x) = cos x

tan (180 - x) = -tan x)

# -x ⇒fourth quadrant (sin (- x) = -sin x , cos (- x) = cos x

tan (- x) = -tan x)

* Lets solve the problem

∵ L. H .S is ⇒ cos x cos (-x) - sin (x) sin (-x)

- From the rules above cos x = cos(-x)

∴ cos x cos (-x) = cos x cos x

∴ cos x cos (-x) = cos² x

- From the rule above sin (-x) = - sin x

∴ sin x sin (-x) = sin x [- sin x]

∴ sin x sin (-x) = - sin² x

∴ cos x cos (-x) - sin (x) sin (-x) = cos² x - (- sin² x)

∴ cos x cos (-x) - sin (x) sin (-x) = cos² x + sin² x

∵ cos² x + sin² x = 1

∴ R.H.S = 1

∴ L.H.S = R.H.S

∴ cos x cos (-x) -sin x sin (-x) = 1

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3 years ago

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1 year ago

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HACTEHA [7]

Answer:

Step-by-step explanation:

Here you go mate

Step 1

-7x+8<-6 Equation/Question

Step 2

-7x+8<-6 Simplify

-7x+8<-6

Step 3

-7x+8<-6 Subtract 8

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Step 4

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answer

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Hope this helps

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2 years ago

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My name is Ann [436]

Answer:

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Step-by-step explanation:

Given

T = 44m + 67

Required

Calculate and interpret the t-intercept

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Hence, the T-intercept is 67

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3 years ago