Question

16
Prove that, tan 50º = tan 40° + 2 tan 10°.
1050​

Answer 1

Answer:

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Step-by-step explanation:

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tan50=tan(40+10)

we have ,tan(a+b)=(tanA+tanB) (1-tanA tanB)

=tan(40+10)=(tan40+tan10)(1-tan40 tan10)

=tan50=(tan40+tan10)(1-tan40 tan10)

=tan50(1-tan40 tan10)=tan40+tan10.

=tan(1-tan40 tan10)=tan40+tan10.

=tan50-tan50 tan40 tan10=tan40+tan10

=and tan50 =tan(90-40)=cot40

=tan50-cot40 tan40 tan10 =tan40+tan10

=tan50-tan10=tan40+tan10

because cot40=1/tan 40

=tan50=tan40+tan10

so, tan50-tan40=2tan10