The minimum value of 2 sin ^{2} theta+3 cos ^ | vedclass

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

Question

(C) Given expression: $2 \sin ^{2} 	heta + 3 \cos ^{2} 	heta$We know that $\sin ^{2} 	heta = 1 - \cos ^{2} 	heta$.Substituting this into the expre

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(C) Given expression: $2 \sin ^{2} 	heta + 3 \cos ^{2} 	heta$We know that $\sin ^{2} 	heta = 1 - \cos ^{2} 	heta$.Substituting this into the expression:$2(1 - \cos ^{2} 	heta) + 3 \cos ^{2} 	heta$$= 2 - 2 \cos ^{2} 	heta + 3 \cos ^{2} 	heta$$= \cos ^{2} 	heta + 2$Since the range of $\cos ^{2} 	heta$ is $[0, 1]$,the minimum value of $\cos ^{2} 	heta$ is $0$.Therefore,the minimum value of the expression is $0 + 2 = 2$.

The minimum value of $2 \sin ^{2} \theta+3 \cos ^{2} \theta$ is

Similar Questions

If $\frac{\sin A - \sin C}{\cos C - \cos A} = \cot B,$ then $A, B, C$ are in

The value of $\sin^{2} \theta + \sin^{2}(\theta + 60^{\circ}) + \sin^{2}(\theta - 60^{\circ}) =$

$(\sec 2A + 1){\sec ^2}A = $

If $x + \frac{1}{x} = 2\cos \theta ,$ then ${x^3} + \frac{1}{{{x^3}}} = $

If $\sin A + \sin^2 A = 1$,then the value of $\cos^2 A + \cos^4 A$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module