Jitender Gupta and Divya Malik Solutions for Exercise 3: CHALLENGERS

If $\sin \alpha$ and $\cos \alpha$ are the roots of the equation $p{x}^2+qx+r=0$, then the value of $p^2-q^2+2rp$is

In $∆ABC$right angled at $B$, if $BC=5\mathrm{cm} \mathrm{and} AC-AB=1\mathrm{cm}$, then the value of $\frac{{\cos }^{2}C}{1-\sin C}$ is

If ${\mathrm{T}}_{\mathrm{n}}= {\sin }^{\mathrm{n}}\mathrm{\theta }+{\cos }^{\mathrm{n}}\mathrm{\theta }$, then the value of $\frac{{\mathrm{T}}_3-{\mathrm{T}}_5}{{\mathrm{T}}_1}$ is

If $\sin \mathrm{\theta }+ {\sin }^2\mathrm{\theta }= 1$ then the value of  ${\cos }^{12}\mathrm{\theta } + 3{\cos }^{10}\mathrm{\theta } + 3{\cos }^8\mathrm{\theta } + {\cos }^6\mathrm{\theta } + 2{\cos }^4\mathrm{\theta }+ 2{\cos }^2\mathrm{\theta }-2$ is:

The value of the expression $1-\frac{{\sin }^{2}y}{1+\cos y}+\frac{1+\cos y}{\sin y}-\frac{\sin y}{1-\cos y}$ ​is.

If $(\sec \mathrm{A}+ \tan \mathrm{A}) (\sec \mathrm{B} + \tan \mathrm{B}) (\sec \mathrm{C} + \tan \mathrm{C}) = (\sec \mathrm{A} -\tan \mathrm{A}) (\sec \mathrm{B} -\tan \mathrm{B}) (\sec \mathrm{C} -\tan \mathrm{C}) = \mathrm{x}$, then the value(s) of $\mathrm{x}$ is/are?

If $\mathrm{f}\left(\mathrm{x}\right)={\cos }^2\mathrm{x}+{\sec }^2\mathrm{x}$, then $\mathrm{f}\left(\mathrm{x}\right)$ is 

If a $\sec \mathrm{\theta }+\mathrm{b} \tan \mathrm{\theta }+ \mathrm{c}= 0 \mathrm{and} \mathrm{p} \sec \mathrm{\theta } + \mathrm{q} \tan \mathrm{\theta } + \mathrm{r} = \mathrm{Q}$  then $(\mathrm{br}-\mathrm{qc}{)}^2- (\mathrm{pc}-\mathrm{ar}{)}^2$ is equal to.