If 2 t a n x = 3 t a n y = 5 t a n z and x + y + z = π , tan 2 x + tan 2 y + tan 2 z = K 38 then K =

tan x = 2 t , tan y = 3 t , tanz = 5 t ∑ tan x = π ( tan x ) ⇒ t 2 = 3 1 tan 2 x + tan 2 y + tan 2 z = t 2 ( 4 + 9 + 25 ) = 38 t 2 , K = 3

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MathematicsTrigonometric Ratios & IdentitiesConditional identitiesMedium2 minQB

MathematicsMediuminteger

If $\frac{t a n x}{2} = \frac{t a n y}{3} = \frac{t a n z}{5}$ and $x + y + z = π, tan^{2} x + tan^{2} y + tan^{2} z = \frac{38}{K}$ then $K =$

Answer:

Solution:

$tan x = 2 t, tan y = 3 t, tanz = 5 t$

$\sum tan x = π (tan x) \Rightarrow t^{2} = \frac{1}{3}$ $tan^{2} x + tan^{2} y + tan^{2} z = t^{2} (4 + 9 + 25) = 38 t^{2}, K = 3$

Stream:JEESubject:MathematicsTopic:Trigonometric Ratios & IdentitiesSubtopic:Conditional identities

⏱ 2mℹ️ Source: QB

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