Minimum value of 5 sin^2 theta + 4 cos^2 thet | vedclass

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

Question

(D) Let $f(	heta) = 5 \sin^2 	heta + 4 \cos^2 	heta$.We know that $\sin^2 	heta + \cos^2 	heta = 1$,so $\cos^2 	heta = 1 - \sin^2 	heta$.Substi

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(D) Let $f(	heta) = 5 \sin^2 	heta + 4 \cos^2 	heta$.We know that $\sin^2 	heta + \cos^2 	heta = 1$,so $\cos^2 	heta = 1 - \sin^2 	heta$.Substituting this into the expression:$f(	heta) = 5 \sin^2 	heta + 4(1 - \sin^2 	heta)$$f(	heta) = 5 \sin^2 	heta + 4 - 4 \sin^2 	heta$$f(	heta) = \sin^2 	heta + 4$.Since the minimum value of $\sin^2 	heta$ is $0$,the minimum value of $f(	heta)$ is $0 + 4 = 4$.

Minimum value of $5 \sin^2 \theta + 4 \cos^2 \theta$ is

Similar Questions

$A$ ladder having a length of $16\,m$ is leaning against a wall at an angle of $60^{\circ}$ with the ground. Find the distance between the wall and the foot of the ladder (in $m$).

If $\sin x + \sin^2 x = 1,$ then $\cos^8 x + 2\cos^6 x + \cos^4 x = $

If $\tan B = \frac{n \sin A \cos A}{1 - n \cos^2 A}$,then $\tan(A + B)$ equals

If $(1+\tan ^{2} \theta)=\frac{625}{49}$ and $\theta$ is acute,then what is the value of $\sqrt{\sin \theta+\cos \theta}$?

If $x \cos \theta - \sin \theta = 1$,then $x^2 - (1 + x^2) \sin \theta$ equals

Vedclass Test Series

Exam Paper Generator

Online Exam Module