Please help me........

Question

asked Jul 5, 2021 29.5k views

1 Answer

Furtive · Answer 1 · 2021-07-09T06:23:40+0000

Answer: see proof below

Explanation:

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

Scratchwork:

tan (50) = tan (40 + 10)

$= (\tan 40+\tan 10)/(1-\tan 40\cdot \tan 10)$

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
$\checkmark$