If tan x 40 deg tan x 20 deg tan 3x deg tan 70 mdash x deg tan 50 mdash x deg I then the value of x ...........

Quantitative Aptitude (CDS) Trignometry

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If tan(x + 40)°tan(x + 20)°tan(3x)°tan(70 — x)°tan(50 —x)° = I, then the value of x is equal to

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Explanation:

tan(x+40)^°tan(x+20)^°tan(3x)°tan(70−x)^°tan(50−x)^°=1
⇒tan[90−(50−x)]^°tan[90−(70−x)]^°tan(3x)^°tan(70−x)^°tan(50−x)^°=1
⇒cot(50−x)^°cot(70−x)^°tan(3x)^°tan(70−x)^°tan(50−x)^°=1
⇒tan(3x)^°=1
⇒tan(3x)^°=tan45^°
⇒3x=45⇒x=15