Question

If 3 x tan(x – 15) = tan(x + 15), then the value of x is​

Answer 1

answer is also in attachment and here too:

Solution -

3tan(θ−15

∘

)=tan(θ+15

∘

)

3=

tan(θ−15

∘

)

tan(θ+15

∘

)

3−1

3+1

=

tan(θ+15

∘

−tan(θ−15

∘

)

tan(θ+15

∘

)+tan(θ−15

∘

)

2=

cos(θ+15

∘

)

sin(θ+15

∘

)

−

cos(θ−15

∘

)

sin(θ−15

∘

)

cos(θ+15

∘

)

sin(θ+15

∘

)

+

cos(θ−15

∘

)

sin(θ−15

∘

)

2=

sin(θ+15

∘

)cos(θ−15

∘

)−sin(θ−15

∘

)cos(θ+15

∘

)

sin(θ+15

∘

)cos(θ−15

∘

)+sin(θ−15

∘

)cos(θ+15

∘

)

Apply sin(A+B)=sinAcosB+cosAsinB

sin(A−B)=sinAcosB−cosAsinB

2=

sin(30

∘

)

sin(2θ)

sin2θ=1

2θ=2nπ+

2

π

θ=nπ+

4

π

in 0<θ<90

∘

−θ=45

∘