Embibe Experts Solutions for Exercise 17: Assignment

If the median of triangle $A B C$ through $A$ is perpendicular $A B$, then the value of $\sin A\cos B+2\sin B\cos A$ is equal to

If $4{\sin }^{4}x+{\cos }^{4}x=1$ and $x\in [-4\pi ,4\pi ]$, then number of real values of $x$ satisfying the given equation is

In a triangle $A B C$, if $a^3\cos (B-C)+b^3\cos (C-A)+c^3\cos (A-B)=360$ . Then $a b c$ is equal to

Area of the triangle is $10\sqrt{3}$ sq. units, angle $C=\frac{\pi }{3}$ and its perimeter is $20$ units, then side $c$ is equal to

In a $∆ABC$, if $\frac{11}{b+c}=\frac{12}{c+a}=\frac{13}{a+b}$, then the value of $\sec C$ is equal to

In triangle $ABC$, if $a^4+b^4+c^4=a^2{b}^2+2b^2{c}^2+2c^2{a}^2$ , then acute angle $C$ is $x°$, then $x$ is equal to

If $r_1,r_2,r_3$ are the radii of excircles of a triangle $ABC$ and $r$ is the inradius, then $r_1{r}_2{r}_3-r\left(r_1{r}_2+r_2{r}_3+r_3{r}_1\right)$ is equal to

In triangle $ABC$, if $r:r_1=2:3$ then the value of $81\tan \frac{A}{2}\left(\tan \frac{B}{2}+\tan \frac{C}{2}\right)$ is equal to