Question
Question: If \(\cos ^ { - 1 } \sqrt { p } + \cos ^ { - 1 } \sqrt { 1 - p } + \cos ^ { - 1 } \sqrt { 1 - q } =...
If cos−1p+cos−11−p+cos−11−q=43π then the value of q is.
A
1
B
21
C
31
D
21
Answer
21
Explanation
Solution
Let α=cos−1p β=cos−11−p
And γ=cos−11−q or cosα=p;cosβ=1−p
and
Thereforesinα=1−p sinβ=p and sinγ=q.
The given equation may be written as
α+β+γ=43π or α+β=43π−γ or
cos(α+β)=cos(43π−γ)
⇒ cosαcosβ−sinαsinβ= cos{π−(4π+γ)}=−cos(4π+γ)
⇒ =−(211−q−21⋅q)
⇒ 1−q=q ⇒