Something new, may be??

Geometry Level 5

If the product of the cosines of angles of Δ A B C \Delta~ ABC is − 0.387 -0.387 . then find

∑ c y c t a n A t a n B \large{\displaystyle \sum_{cyc} tanA tanB}

Answer upto three decimals


The answer is -1.584.

Tanishq Varshney by Tanishq Varshney , 23, India

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1 solution

Tanishq Varshney
Apr 6, 2015

For me it was new

c o s ( A + B + C ) = c o s A c o s B c o s C ( 1 − ∑ t a n A t a n B ) cos(A+B+C)=cosAcosBcosC(1-\sum tanA tanB)

A + B + C = π A+B+C=\pi

I hope its understood t a n A t a n B + t a n B t a n C + t a n C t a n A = ∑ t a n A t a n B tanAtanB+tanBtanC+tanCtanA=\sum tanA tanB

5 Helpful 0 Interesting 0 Brilliant 0 Confused

That's a very nice application of the formula..

Ayush Garg - 6 years, 2 months ago

Mention that it is cyclic sum.

Vishnu Bhagyanath - 5 years, 11 months ago

never knew of that identity, i just assumed 2 of 3 angles are equal to simplify calculation, the third angle must be obtuse

Vincent Miller Moral - 4 years, 4 months ago

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