Prove that $cos^2\theta. sin^4\theta=…$ February 11

Prove that: $$cos^2\theta.sin^4\theta=\frac{1}{32}(cos6\theta-cos2\theta+cos4\theta)$$Attempt: $$L.H.S=cos^2\theta.sin^4\theta$$ $$=cos^2\theta.sin^2\theta.sin^2\theta$$ $$=\frac{1+cos2\theta}{2}.\frac{1-cos2\theta}{2}.\frac{1-cos2\theta}{2}$$ $$=

A small doubt in metric space. February 11    1

Is $\mathbb{R}$ an open ball in $\mathbb{R}$?If we write B(0,$\infty$) as the open ball then $\mathbb{R}$ is an open ball in $\mathbb{R}$. Is it correct?Thanks.No, balls have finite radius. It is an open set however.1 4

A reduction of $10%$… February 11

A reduction of $10%$ % in the price of sugar would enable a man to buy $2$ kgs of sugar more for Rs.$125$. Find the reduced price per kg.My attempt: Let the initial price of sugar be Rs. $x$ kg.Price after $10%$ % reduction $$=x-10 percent of x$$ $$=

How to fit sum of products of sine waves February 11

System Model:$Y(t_1, t_2, t_3) = A*[2+k_1*cos(w_1t_1+\phi_1)+k_2*cos(w_2t_2+\phi_2)+4*k_3*cos(\dfrac{w_1t_1+\phi_1}{2})*cos(\dfrac{w_2t_2+\phi_2}{2})*cos(\dfrac{w_1t_1+\phi_1-w_2t_2-\phi_2}{2}-w_3t_3-\phi_3)]$Conditions:A>0$ -1 \leq k_1,k_2 \leq 1$$0

Linear Algebra. Is this question realte to combination and factorials February 11

Linear Algebra. Is this question realte to combination and factorials
I am not able to understand this question and what is the entries of matrix A exactly. Question Thanks.

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