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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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