If ≤ft(A/2)={1+a/1-a}·≤ft(θ/2), then cos θ=

Correct Answer is : cos⁡A−a1−acos⁡A A - a/1 - a A1−acosAcosA−a

Correct Answer is : cos⁡A−a1−acos⁡A A - a/1 - a A1−acosAcosA−a

Test Index

TS EAMCET 14-Sep-2020 Shift 2 Solved Paper

Section: Mathematics

Question : 22 of 160

Marks: +1, -0

\cot\left(\frac{A}{2}\right)=\sqrt{\frac{1+a}{1-a}}\cdot\cot\left(\frac{\theta}{2}\right)

, then cos θ=

Solution:

We have,

\cot\frac{A}{2}=\sqrt{\frac{1+a}{1-a}}\cot\frac{\theta}{2}

\Rightarrow

\cot^{2}\frac{A}{2}=\left(\frac{1+a}{1-a}\right)\cot^{2}\frac{\theta}{2}

\Rightarrow \left(\frac{\cos^{2}\frac{A}{2}}{\sin^{2}\frac{A}{2}}\right)\left(\frac{1-a}{1+a}\right)=\frac{\cos^{2}\frac{\theta}{2}}{\sin^{2}\frac{\theta}{2}}

\Rightarrow \frac{(1+\cos A)(1-a)}{(1-\cos A)(1+a)}=\frac{1+\cos\theta}{1-\cos\theta}

\Rightarrow \frac{1-a-a\cos A+\cos A}{1+a-a\cos A-\cos A}=\frac{1+\cos\theta}{1-\cos\theta}

Apply componendo and dividendo,

\Rightarrow \frac{2(1-a\cos A)}{2(\cos A-a)}=\frac{2}{2\cos\theta}\Rightarrow \cos\theta=\frac{\cos A-a}{1-a\cos A}

Go to Question:

Prev Question

Next Question