Embibe Experts Solutions for Chapter: Advance Maths, Exercise 2: Exercise 2

Simplify: $\frac{{\left(\sin \mathrm{\theta }+\sec \mathrm{\theta }\right)}^2+{\left(\cos \mathrm{\theta }+\mathrm{cosec} \mathrm{\theta }\right)}^2}{{\left(1+\sec \mathrm{\theta } \mathrm{cosec} \mathrm{\theta }\right)}^2}, 0^{\mathrm{o}}<\mathrm{\theta }<{90}^{\mathrm{o}}$

If ${\sin }^2\theta =2\sin \theta -1, 0°\le \theta \le 90°$, then find the value of $\frac{1+\cos ec\theta }{1-\cos \theta }$.

If $\frac{\sin \theta +\cos \theta }{\sin \theta -\cos \theta }=5$, then the value of $\frac{4 {\sin }^2\theta +3}{2 co{s}^2\theta +2}$ is_______.

If $\mathrm{sin\alpha }+\mathrm{sin\beta }=\mathrm{cos\alpha }+\mathrm{cos\beta }=1$, then $\mathrm{sin\alpha }+\mathrm{cos\alpha }=?$

If x is a real quantity, what is the minimum value of $\left(25{\cos }^2\mathrm{x}+9{\sec }^2\mathrm{x}\right)?$

If $\mathrm{Cot} \mathrm{\theta }=\frac{15}{8}, \mathrm{\theta }$ is an acute angle, then find the value of $\frac{(1-\cos \theta )(2+2\cos \theta )}{(2-2\sin \theta )(1+\sin \theta )}$

If $\tan \left(\mathrm{A}\right)=\frac{1}{2}$ and $\tan \left(\mathrm{B}\right)=\frac{1}{3}$so find the value of $\mathrm{A}+\mathrm{B}$;

If $\frac{1}{1-\mathrm{sin\theta }}+\frac{1}{1+\mathrm{sin\theta }}=4\mathrm{sec\theta }, 0°<\mathrm{\theta }<90°$, then the value of $\cot \mathrm{\theta }+\mathrm{cosec} \mathrm{\theta }$ is: