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Prove the following : tan6^@.tan42^@.tan66^@.tan78^@ = 1 |
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Answer» SOLUTION :We have TAN3A = tanAtan(60^@-A)tan(60^@+A) Now putting `A=6^@` and `18^@`. in (1) we have `tan18^@=tan6^@tan54^@tan66^@......(2) and `tan54^@` =`tan18^@tan42^@tan78^@` ......(3) Multiplying (2) and (3) we have `tan18^@tan54^@` =`tan6^@tan54^@tan66^@tan18^@tan42^@tan78^@` or, 1=`tan6^@tan42^@tan66^@tan78^@`. |
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