JEE Main 2014 · 11 Apr · Shift 1 · Mathematics Q88

← JEE Main 2014 · 11 Apr · Shift 1

MathematicsSingle correct+4 / -1Question 88 of 90

If $2\cos\theta+\sin\theta=1$ $\left(\theta\ne\dfrac\pi2\right)$ , then $7\cos\theta+6\sin\theta$ is equal to :

\dfrac12

\dfrac{11}2

\dfrac{46}5

Answer and worked solution

Official answer: B

$\sin\theta=1-2\cos\theta$ , and squaring gives $5\cos^2\theta=4\cos\theta$ . So $\cos\theta=\frac45$ ( $\cos\theta=0$ is excluded), and $\sin\theta=-\frac35$ .
$7\cos\theta+6\sin\theta=\frac{28-18}5=2.$

Topics:Trigonometric equations Trigonometric ratios and identities

← Previous question Next question →

JEE Main 2014 · 11 Apr · Shift 1, Mathematics question 88