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3 years ago

Please help me........

Mathematics

1 answer:

Alenkasestr [34]3 years ago

8 0

Answer: see proof below

Step-by-step explanation:

Use the Sum/Difference Identity: tan (A + B) = (tanA + tanB)/(*1 - tanA · tanB)

Scratchwork:

tan (50) = tan (40 + 10)

$= \dfrac{\tan 40+\tan 10}{1-\tan 40\cdot \tan 10}$

tan 50 (1 - tan 40 · tan 10) = tan 40 + tan 10

tan 50 - tan 50 · tan 40 · tan 10 = tan 40 + tan 10

tan 50 = tan 40 + tan 10 + tan 50 · tan 40 · tan 10

Use the Reciprocal Identity: cot A = 1/ tan --> cot A · tan A = 1

Proof LHS → RHS

LHS: tan 50 - tan 40

Substitute tan 50: tan 40 + tan 10 + (tan 50 · tan 40) · tan 10 - tan 40

Simplify: tan 10 + (tan 50 · tan 40) · tan 10

Reciprocal Identity: tan 10 + tan 10

Simplify: 2 tan 10

LHS = RHS: 2 tan 10 = 2 tan 10 $\checkmark$

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Which equation is equivalent to √x^2+81 = x+10

jeka57 [31]

Keywords:

equation, operations, equivalent, binomial, square root

For this case we have an equation in which we must apply operations to rewrite it in an equivalent way. We must start by raising both sides of the equation to the square. Thus, we eliminate the square root of the left side of equality and finally solve the binomial of the right side of equality.

So we have:

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