Question

prove that tan50°-tan 40°=2tan 10°​

Answer 1

Step-by-step explanation:

Tan50-tan40=2tan10

tan50=2tan+tan90

tan50=tan[40+10]

we have tan[a+b]=[tan a+tan b]

[1-tan a tan b]

=tan[40+10]=[tan40+tan10]

[1-tan40 tan10]

=tan50=[tan40+tan10]

[1-tan40tan10]

=tan50[1-tan40tan10]=tan40+tan10

=tan50-tan50tan40tan10=tan40+tan10....and

tan50=tan[90-40]=cot40

=tan50-cot90tan40tan10=tan40+tan10

=tan50-tan10=tan40+tan10

because cot90=1

tan40

=tan50=tan40+2tan10

.

· · tan50-tan40=2tan10

Answer 2

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