Using Fundamental Identities

In mathematics, fundamental identities serve as the critical formulas that establish a connection between varying mathematical values. They are the essence of trigonometry, aiding in the simplification of intricate expressions and the resolution of equations. Essential identities encompass reciprocal, quotient, Pythagorean, co-function, even/odd, and double/half angle identities. Acquiring a thorough understanding of these is an essential step towards tackling more sophisticated mathematical challenges.

The problems about Using Fundamental Identities

Topic	Problem	Solution
None	Find $\cos (2 A)$ , if $\cos (A) = - \frac{21}{29}$ , …	We are given that $\cos (A) = - \frac{21}{29}$ and that $A$ is in the third quadrant.
None	Find $\cos (2 A)$ , if $\cos (A) = - \frac{21}{29}$ , …	We are given that $\cos (A) = - \frac{21}{29}$ and that $A$ is in quadrant 3.
None	Find $\cos (2 A)$ , if $\cos (A) = - \frac{21}{29}$ , …	Given that $\cos (A) = - \frac{21}{29}$ and $A$ is in quadrant 3
None	Let $\cos A = - \frac{2}{\sqrt{13}}$ with $A$ in $Q …	Given that $\cos A = - \frac{2}{\sqrt{13}}$ with A in Quadrant III, we are asked to find \(\cot (2…
None	Use identities to find values of the sine and cos…	We are given that $\tan x = - 2$ and $\cos x < 0$ .
None	Decide whether the statement is possible or impos…	Decide whether the statement is possible or impossible: $\cos α = - \frac{1}{2}$ and \(\sec \al…
None	Use an identity to write the expression as a sing…	Given the expression $\frac{1}{6} - \frac{1}{3} \sin^{2} {35.9}^{\circ}$
None	Use identities to fill in the blank. If $\tan \th…	The cotangent of an angle is the reciprocal of the tangent of that angle.
None	Use the appropriate reciprocal identity to find t…	We are given that $\csc θ = \frac{\sqrt{63}}{7}$
None	Use a double-angle identity to find the exact val…	The given expression is in the form of a double angle identity for cosine. The double angle identit…
None	Find the expression that is equivalent to $\frac{…	The given expression is \(\frac{\tan \frac{3 \pi}{4}+\tan \frac{\pi}{6}}{1-\tan \frac{3 \pi}{4} \ta…
None	Find the exact value of the expression by using a…	Let's denote $a = \sin 72^{\circ}$ and $b = \cos 42^{\circ}$ . Then we have \(\sin 72^\circ \cos 42^…
None	Use identities to correctly complete the sentence…	The tangent of an angle is defined as the ratio of the sine of the angle to the cosine of the angle…