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2 years ago

PLEASE HELP WITH STEPS 25 POINTS!!!! Simplify

Mathematics

1 answer:

valentinak56 [21]2 years ago

5 0

Answer:

- 1 - sin α

Step-by-step explanation:

Use identity:

sin² α + cos² α = 1 ⇒ cos² α = 1 - sin² α = (1 + sin α)(1 - sin α)

Substitute this into given expression and simplify:

cos² α / (sin α - 1) =
(1 + sin α)(1 - sin α) / (sin α - 1) =
- (1 + sin α) =
- 1 - sin α

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Solving inequalities for word problems:

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For this case we have to:

x: Let the variable representing the unknown number

We algebraically rewrite the given expression:

Twice a number plus 10, is represented as: $2x + 10$

Three times that number less 4. is represented as:

$3x-4$

Thus, the complete expression is:

$2x + 10> 3x-4$

Subtracting 3x from both sides of the inequality:

$2x-3x + 10> -4\\-x + 10> -4$

Subtracting 10 from both sides of the inequality:

$-x> -4-10$

Equal signs are added and the same sign is placed:

$-x> -14$

We multiply by -1 on both sides, taking into account that the sense of inequality changes:

$x$

The solution is given by all values of "x" less than 14.

Answer:

$x$

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2 years ago