TG EAPCET 2024 (Online) 10th May Evening Shift | Trigonometric Equations Question 1 | Mathematics

Suppose, $\theta_{1}$ and $\theta_{2}$ are such that $\left(\theta_{1}-\theta_{2}\right)$ lies in 3rd or 4th quadrant. If $\sin \theta_{1}+\sin \theta_{2}=-\frac{21}{65}$ and $\cos \theta_{1}+\cos \theta_{2}=-\frac{27}{65}$, then $\cos \left(\frac{\theta_{1}-\theta_{2}}{2}\right)=$

$\frac{3}{\sqrt{150}}$

$\frac{3}{\sqrt{130}}$

$-\frac{3}{\sqrt{130}}$

$-\frac{3}{\sqrt{150}}$

TG EAPCET 2024 (Online) 10th May Evening Shift

MCQ (Single Correct Answer)

-0

If $A$ is the solution set of the equation $\cos ^{2} x=\cos ^{2} \frac{\pi}{6}$ and $B$ is the solution set of the equation $\cos ^{2} x=\log _{16} P$ where, $P+\frac{16}{P}=10$, then, $B-A=$

$\left\{x \in R / x=2 n \pi \pm \frac{\pi}{4}, 2 n \pi \pm \frac{\pi}{3} n=0,12,3 \ldots\right\}$

$\left\{x \in R / x=2 n \pi \pm \frac{\pi}{3}, 2 n \pi \pm \frac{2 \pi}{3} n=0,1,2,3 \ldots\right\}$

$\left\{x \in R / x=2 n \pi \pm \frac{\pi}{6}, 2 n \pi \pm \frac{\pi}{12} n=0,1,2,3 \ldots\right\}$

$\left\{x \in R / x=2 n \pi \pm \frac{\pi}{8}, 2 n \pi \pm \frac{\pi}{16} n=0,1,2,3 \ldots\right\}$

TG EAPCET 2024 (Online) 10th May Morning Shift

MCQ (Single Correct Answer)

-0

If $\tan A+\tan B+\cot A+\cot B=\tan A \tan B-\cot A \cot B$ and $0^{\circ} < A+B<270^{\circ}$, then $A+B=$

$45^{\circ}$

$135^{\circ}$

$150^{\circ}$

$225^{\circ}$

TG EAPCET 2024 (Online) 10th May Morning Shift

MCQ (Single Correct Answer)

-0

The equation that is satisfied by the general solution of the equation $4-3 \cos ^2 \theta=5 \sin \theta \cos \theta$ is

$7 \sin ^2 \theta+3 \cos ^2 \theta=4$

$\sin ^2 \theta-2 \cos \theta+\frac{1}{4}=0$

$\cot \theta-\tan \theta=\sec \theta$

$1+\sin ^2 \theta=3 \cos ^2 \theta$

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