Embibe Experts Solutions for Chapter: Trigonometric Ratios, Functions and Identities, Exercise 1: Exercise-1

If $f\left(\theta \right)={\sin }^4\theta +{\cos }^2\theta ,$ then range of $f\left(\theta \right)$ is

Range of function $f\left(x\right)={\cos }^{2}x+4{\sec }^{2}x$ is

The difference between maximum and minimum value of the expression $y=1+2\sin x+3{\cos }^{2}x$ is

The greatest and least value of $y=10{\cos }^{2}x-6\sin x\cos x+2{\sin }^{2}x$ are respectively,

A triangle $ABC$ is such that $\sin (2A+B)=\frac{1}{2}.$ If $A, B, C$ are in A.P. then the angle $A, B, C$, are respectively.

$\left(\mathrm{iv}\right) {\left(a-b\right)}^2{\cos }^2\frac{C}{2}+{\left(a+b\right)}^2{\sin }^2\frac{C}{2}=c^2$

$\left(\mathrm{v}\right)$ $b^2\sin 2C+c^2\sin 2B=2bc\sin A$

$\left(\mathrm{iii}\right)$ $\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}=\frac{1}{2Rr}$