# Trigonometric identities questions and answers

Recent questions in Trigonometric equation and identitie
Trigonometric equation and identitie

### Proof trigonometric identities. $$\displaystyle{\frac{{{1}-{\sin{{\left(-{x}\right)}}}}}{{{\cos{{x}}}+{\cos{{\left(-{x}\right)}}}{\sin{{x}}}}}}={\sec{{x}}}$$

Trigonometric equation and identitie

### Verify the identity $$\displaystyle{\tan{\times}}{{\csc}^{{2}}{x}}–{\tan{{x}}}={\cot{}}$$

Trigonometric equation and identitie

### Verify the identity. $$\displaystyle{\sin{{2}}}{x}{\cos{{x}}}-{\cos{{2}}}{x}{\sin{{x}}}={\sin{{x}}}$$

Trigonometric equation and identitie

### Establish identity $$\displaystyle{1}-{\frac{{{{\cos}^{{2}}\theta}}}{{{1}+{\sin{\theta}}}}}={\sin{\theta}}$$

Trigonometric equation and identitie

### Proof trigonometry identities. $$\displaystyle{\cot{{\left({x}\right)}}}+{\tan{{\left({x}\right)}}}+{\sec{{\left({x}\right)}}}{\csc{{\left({x}\right)}}}={2}{\sec{{\left({x}\right)}}}{\csc{{\left({x}\right)}}}$$

Trigonometric equation and identitie

### Prove the identity whether is true or false $$\displaystyle{\cos{{2}}}\theta={\frac{{{1}-{{\tan}^{{2}}\theta}}}{{{1}+{{\tan}^{{2}}\theta}}}}$$

Trigonometric equation and identitie

### Proved the trigonometry identity $$\displaystyle{\frac{{{{\csc}^{{2}}{x}}}}{{{{\cot}^{{2}}+}{{\sec}^{{2}}{x}}+{1}}}}={{\cos}^{{2}}{x}}$$

Trigonometric equation and identitie

### Prove the identity $$\displaystyle{\frac{{{1}}}{{{2}{\csc{{2}}}{x}}}}={{\cos}^{{2}}{x}}{\tan{{x}}}$$ Choose the sequence of steps below that verifies the identity A) $$\displaystyle{{\cos}^{{2}}{x}}{\tan{{x}}}={{\cos}^{{2}}{x}}{\frac{{{\sin{{x}}}}}{{{\cos{{x}}}}}}={\cos{{x}}}{\sin{{x}}}={\frac{{{\sin{{2}}}{x}}}{{{2}}}}={\frac{{{1}}}{{{2}{\csc{{2}}}{x}}}}$$ B) $$\displaystyle{{\cos}^{{2}}{x}}{\tan{{x}}}={{\cos}^{{2}}{x}}{\frac{{{\cos{{x}}}}}{{{\sin{{x}}}}}}={\cos{{x}}}{\sin{{x}}}={\frac{{{\sin{{2}}}{x}}}{{{2}}}}={\frac{{{1}}}{{{2}{\csc{{2}}}{x}}}}$$ C) $$\displaystyle{{\cos}^{{2}}{x}}{\tan{{x}}}={{\cos}^{{2}}{x}}{\frac{{{\cos{{x}}}}}{{{\sin{{x}}}}}}={\cos{{x}}}{\sin{{x}}}={2}{\sin{{2}}}{x}={\frac{{{1}}}{{{2}{\csc{{2}}}{x}}}}$$ D) $$\displaystyle{{\cos}^{{2}}{x}}{\tan{{x}}}={{\cos}^{{2}}{x}}{\frac{{{\sin{{x}}}}}{{{\cos{{x}}}}}}={\cos{{x}}}{\sin{{x}}}={2}{\sin{{2}}}{x}={\frac{{{1}}}{{{2}{\csc{{2}}}{x}}}}$$

Trigonometric equation and identitie

### Verify the identify. $$\displaystyle{\frac{{{{\csc}^{{2}}\theta}}}{{{1}+{{\tan}^{{2}}\theta}}}}={{\cot}^{{2}}\theta}$$

Trigonometric equation and identitie

### Establish identity $$\displaystyle{\frac{{{\csc{{v}}}-{1}}}{{{\csc{{v}}}+{1}}}}={\frac{{{1}-{\sin{{v}}}}}{{{1}+{\sin{{v}}}}}}$$

Trigonometric equation and identitie

### Prove that of the two trigonometric equations. $$\displaystyle{\tan{{\left({A}+{B}\right)}}}={\frac{{{\tan{{A}}}+{\tan{{B}}}}}{{{1}-{\tan{{A}}}{\tan{{B}}}}}}$$ $$\displaystyle{\sin{{2}}}\theta={2}{\sin{\theta}}{\cos{\theta}}$$

Trigonometric equation and identitie

### Verify that the equation is an identity. $$\displaystyle{\frac{{{\cos{\theta}}+{1}}}{{{{\tan}^{{2}}\theta}}}}={\frac{{{\cos{\theta}}}}{{{\sec{\theta}}-{1}}}}$$

Trigonometric equation and identitie

### Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 11 passengers per minute.

Trigonometric equation and identitie

### Prove the identity $$\frac{1}{2\csc 2x}=\cos^2 x \tan x$$ Choose the sequence of steps below that verifies the identity A) $$\cos^2 x \tan x =\cos^2 x \frac{\sin x}{\cos x}=\cos x \sin x =\frac{\sin 2x}{2}=\frac{1}{2\csc 2x}$$ B) $$\cos^2 x \tan x=\cos^2 x \frac{\cos x}{\sin x}=\cos x \sin x=\frac{\sin 2x}{2}=\frac{1}{2 \csc 2x}$$ C) $$\cos^2 x \tan x=\cos^2 x \frac{\cos x}{\sin x}=\cos x \sin x=2 \sin 2x=\frac{1}{2 \csc 2x}$$ D) $$\cos^2 x \tan x =\cos^2 x \frac{\sin x}{\cos x}=\cos x \sin x=2 \sin 2x=\frac{1}{2 \csc 2x}$$

Trigonometric equation and identitie

### (1,5 points) Find the intervals of concavity and the inflection points of the function $$\displaystyle{f{{\left({x}\right)}}}={x}{\left({2}{x}−{1}\right)}^{{2}}$$

Trigonometric equation and identitie

### $$\displaystyle{\left({\sin{{x}}}+{\cos{{x}}}\right)}²={1}+{\sin{{2}}}{x}$$

Trigonometric equation and identitie

### Verify that the equation is an identity. (Hint: $$\cos2x=\cos(x+x)$$.) $$\cos2x+2\sin^{2}x-1=0$$

Trigonometric equation and identitie

### If J is jointly proportional to G and V, and J = √3 when G = √2 and V = √8, what is J when G = √6 and V = 8?

Trigonometric equation and identitie