Mathematics
09.07.2022 21:06
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erenackermanlevijaeg
erenackermanlevijaeg
5,0(57 marks)

 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

     


Please help me........
Please help me........
reagriffis24
reagriffis24
4,8(32 marks)

B. 2

Step-by-step explanation: 14 + -12 = 2

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