If 1+cos^{2} theta = 3 sin theta cos theta,th | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given equation: $1 + \cos^{2} 	heta = 3 \sin 	heta \cos 	heta$.Divide both sides by $\cos^{2} 	heta$ (since $\cos 	heta 
eq 0$ for $0 < 	he

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(B) Given equation: $1 + \cos^{2} 	heta = 3 \sin 	heta \cos 	heta$.Divide both sides by $\cos^{2} 	heta$ (since $\cos 	heta 
eq 0$ for $0 $\frac{1}{\cos^{2} 	heta} + \frac{\cos^{2} 	heta}{\cos^{2} 	heta} = 3 \frac{\sin 	heta \cos 	heta}{\cos^{2} 	heta}$.$\sec^{2} 	heta + 1 = 3 	an 	heta$.Using the identity $\sec^{2} 	heta = 1 + 	an^{2} 	heta$:$(1 + 	an^{2} 	heta) + 1 = 3 	an 	heta$.$	an^{2} 	heta - 3 	an 	heta + 2 = 0$.Factor the quadratic equation:$(	an 	heta - 1)(	an 	heta - 2) = 0$.So,$	an 	heta = 1$ or $	an 	heta = 2$.If $	an 	heta = 1$,then $\cot 	heta = \frac{1}{	an 	heta} = 1$.If $	an 	heta = 2$,then $\cot 	heta = \frac{1}{2} = 0.5$.Since the question asks for the integral value,the correct value is $1$.

If $1+\cos^{2} \theta = 3 \sin \theta \cos \theta$,then the integral value of $\cot \theta$ is $(0 < \theta < \frac{\pi}{2})$.

Similar Questions

If $\sec \theta + \tan \theta = p,$ then $\tan \theta$ is equal to

If $\tan A = \frac{1}{2}$ and $\tan B = \frac{1}{3},$ the value of $A + B$ is

If $A = \cos^2 \theta + \sin^4 \theta$,then for all values of $\theta$:

If $a \cos^3 \alpha + 3a \cos \alpha \sin^2 \alpha = m$ and $a \sin^3 \alpha + 3a \cos^2 \alpha \sin \alpha = n$,then $(m + n)^{2/3} + (m - n)^{2/3}$ is equal to

If $m$ and $M$ are the minimum and the maximum values of $4 + \frac{1}{2} \sin^2 2x - 2 \cos^4 x$ for $x \in R$,then $M - m$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module