If each of - - - - is a positive acute angle such that sin - - - 12- cos- - -12 and tan- - - - -1- find the value of - - -

sin(α+β γ)=12=sin 30^o α +β γ = 30^o #160; #160; #160; ........(1) cos (β +γ α) =12=cos 60^o β +γ α =60^o #160; #160; # ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios of Multiples of an Angle

If each of ...

Question

If each of $α, β, γ$ is a positive acute angle such that
$sin (α + β - γ) = \frac{1}{2}, cos (β + γ - α) = \frac{1}{2}$ and $tan (γ + α - β) = 1$ , find the value of $α, β, γ$ .

Open in App

Solution

$sin (α + β - γ) = \frac{1}{2} = sin 30^{o}$

$α + β - γ = 30^{o}$ ........(1)

$cos (β + γ - α) = \frac{1}{2} = cos 60^{o}$

$β + γ - α = 60^{o}$ ..........(2)

$tan (γ + α - β) = 1 = tan 45^{o}$

$γ + α - β = 45^{o}$ .........(3)

Now, solving these three equations, we get,
$α = 37 {\frac{1}{2}}^{o}, β = 45^{o}$ and $γ = 52 {\frac{1}{2}}^{o}$

Suggest Corrections

Similar questions

In each of $α$ $β$ and $γ$ $is a positive acute angle such that$
$sin (α + β - γ) = \frac{1}{2}, cos (β + γ - α) = \frac{1}{2} and tan (γ + α - β) = 1$
Find the values of $α$ , $β$ , & $γ$ .

Q. If

α, β, γ \in [0, 2 π]

, then the sum of all possible values of

α, β, γ

sin α = - \frac{1}{\sqrt{2}}

cos β = - \frac{1}{2}

tan γ = - \sqrt{3}

, is

Q. If

α, β, γ ϵ [0, 2 π]

, then sum of all positive values of

α, β, γ

if,

sin α = \frac{- 1}{\sqrt{2}}

cos β = \frac{- 1}{2}

tan γ = - \sqrt{3}

, is

Q. Assertion :The minimum value of the expression

sin α + sin β + sin γ

where

α, β, γ

are real numbers such that

α + β + γ = π

is negative. Reason: If

α + β + γ = π

,then

α, β, γ

are the angles of a triangle.

cos (α + β + γ) + cos (α - β - γ) + cos (β - γ - α) + cos (γ - α - β) =

Join BYJU'S Learning Program

If each of α,β,γ is a positive acute angle such thatsin(α+β−γ)=12,cos(β+γ−α)=12 and tan(γ+α−β)=1, find the value of α,β,γ.

sin(α+β−γ)=12=sin30oα+β−γ=30o ........(1)cos(β+γ−α)=12=cos60oβ+γ−α=60o ..........(2)tan(γ+α−β)=1=tan45oγ+α−β=45o .........(3)Now, solving these three equations, we get,α=3712o,β=45o and γ=5212o

If each of $α, β, γ$ is a positive acute angle such that
$sin (α + β - γ) = \frac{1}{2}, cos (β + γ - α) = \frac{1}{2}$ and $tan (γ + α - β) = 1$ , find the value of $α, β, γ$ .