prove that tan 50-tan 40=2 tan 10
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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
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