7.05 Trigonometric identities

Interactive practice questions

Which of the following options correctly completes the identity?

$\tan z=\editable{}$tanz=

$\cot z$cotz

$\frac{\cos z}{\sin z}$coszsinz

$\frac{\sin z}{\cos z}$sinzcosz

$\frac{1}{\cot x}$1cotx

Easy

< 1min

Given that $\sin x=\frac{4}{5}$sinx=45 and $\cos x=\frac{3}{5}$cosx=35, find $\tan x$tanx.

Easy

< 1min

Use properties of the trigonometric functions to find the exact value of $\tan10^\circ-\frac{\sin10^\circ}{\cos10^\circ}$tan10°−sin10°cos10°

Easy

< 1min

Given that $\cos x=\frac{15}{17}$cosx=1517 and $\tan x=\frac{8}{15}$tanx=815, find $\sin x$sinx.

Easy

1min

Use the relationships sin^2 A + cos^2 A = 1, sec^2 A = 1 + tan^2 A, cosec^2 A = 1 + cot^2 A, sinA/cosA = tan A and cosA/sinA = cotA.

Prove simple trigonometric identities.