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prove that tan5+tan40+tan40tan5=1 how to prove this

prove that
tan5+tan40+tan40tan5=1 
how to prove this
 

Grade:11

1 Answers

Vikas TU
14149 Points
7 years ago
Let the given eqn. be like:
tan5+tan40 = 1 – tan40tan5.....................(1)

From tan(x +y) = (tanx+ tany)/(1 – tanx*tany)
 or

tan(x + y) * (1 – tanx * tany) = (tanx + tany)
Put x= 5 and y = 40

tan(45) * (1 -tan5 * tan40) = (tan5 + tan40)
 (1 -tan5 * tan40) = (tan5 + tan40)
Hence proved

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