Answer: tan 2 2 α cot −1 ( cosα )−tan −1 ( cosα )=x 2 π −tan −1 ( cosα )−tan −1 ( cosα )=x (because cot −1 x+tan −1 x= 2 π ) ⇒ 2 π −2tan −1 ( cosα )=x ⇒sinx=sin( 2 π −2tan −1 ( cosα )) Let’s say tan −1 ( cosα )=θ ⇒tanθ= cosα sinx=sin( 2 π −2θ)=cos2θ = 1+tan 2 θ 1−tan 2 θ = 1+cosα 1−cosα sinx= 1+cosα 1−cosα = 2cos 2 α/2 2sin 2 α/2 ⇒sinx=tan 2 2 α . Step-by-step explanation: this answer helpful for u Reply
Answer:
tan
2
2
α
cot
−1
(
cosα
)−tan
−1
(
cosα
)=x
2
π
−tan
−1
(
cosα
)−tan
−1
(
cosα
)=x (because cot
−1
x+tan
−1
x=
2
π
)
⇒
2
π
−2tan
−1
(
cosα
)=x
⇒sinx=sin(
2
π
−2tan
−1
(
cosα
))
Let’s say tan
−1
(
cosα
)=θ
⇒tanθ=
cosα
sinx=sin(
2
π
−2θ)=cos2θ
=
1+tan
2
θ
1−tan
2
θ
=
1+cosα
1−cosα
sinx=
1+cosα
1−cosα
=
2cos
2
α/2
2sin
2
α/2
⇒sinx=tan
2
2
α
.
Step-by-step explanation:
this answer helpful for u