Trigonometric Identities are useful whenever trigonometric functions are involved in an expression or an equation. This activity is designed for students to practice recognizing and simplifying trigonometric identities. Solution: We manipulate the left side to express it in terms of \(\sec \theta \) and \(\tan \theta \). Trigonometric Identities will allow you to remember quickly the most common trigonometric identities that we use in maths and related studies like calculus or algebra. \end{align} \], \[\left( {1 + \frac{1}{{{{\tan }^2}\theta }}} \right)\left( {1 + \frac{1}{{{{\cot }^2}\theta }}} \right) = \frac{1}{{{{\sin }^2}\theta - {{\sin }^4}\theta }}\], \[\begin{align}&LHS = (1 + {\cot ^2}\theta )\left( {1 + {{\tan }^2}\theta } \right)\\ &\qquad\;= {\text{cosec}^2}\theta \times {\sec ^2}\theta \\ &\qquad\;= \frac{1}{{{{\sin }^2}\theta\, {{\cos }^2}\theta }}\\ &\qquad\;= \frac{1}{{{{\sin }^2}\theta\; (1 - {{\sin }^2}\theta )}}\\ &\qquad\;= \frac{1}{{{{\sin }^2}\theta - {{\sin }^4}\theta }} \;= RHS\end{align}\], \[\frac{{1 - \cos \theta }}{{1 + \cos \theta }} = {\left( {\text{cosec}\,\theta - \cot \theta } \right)^2}\], Solution: Let’s start with the right side, \[\begin{align}&RHS = {\left( {\frac{1}{{\sin \theta }} - \frac{{\cos \theta }}{{\sin \theta }}} \right)^2}\\ &\qquad\;\;= {\left( {\frac{{1 - \cos \theta }}{{\sin \theta }}} \right)^2}\\ &\qquad\;\;= \frac{{{{\left( {1 - \cos \theta } \right)}^2}}}{{{{\sin }^2}\theta }}\\ &\qquad\;\;= \frac{{{{\left( {1 - \cos \theta } \right)}^2}}}{{1 - {{\cos }^2}\theta }}\\ &\qquad\;\;= \frac{{{{\left( {1 - \cos \theta } \right)}^2}}}{{(1 + \cos \theta )(1 - \cos \theta )}}\\ &\qquad\;\;= \frac{{1 - \cos \theta }}{{1 + \cos \theta }} = LHS\end{align}\]. Important Angles, Reference the Quadrant in Which an Angle Lies, Trigonometric Students cut out the shapes in the printout and put them together by matching questions and answers on corresponding sides to create the shape in the given solution. Identities, Trigonometric JEE Trigonometry Problem 1, Using the Pythagorean Theorem to find This is a fun way to practice these trig identities to build up a thorough knowledge of the identities.

Trigonometric Equations, The This app allows you to read electrocardiogram data from the BlueHearth Device. Cartesian Plane. There is a printable worksheet available for download here so you can take the quiz with pen and paper. It plays an important role in surveying, Students, teachers and rockstars alike all come here to create and learn.

$3.00. Included with the puzzle pieces is a completed solution answer key. The selection of questions has been selected to help review and achieve mastery of the basic trig … © 2006 - 2020 PurposeGames. Step by step solutions and formulas. This will enable us to factorize the numerator: \[\begin{align}&LHS = \frac{{\left( {\tan \theta + \sec \theta } \right) - \left( {{{\sec }^2}\theta - {{\tan }^2}\theta } \right)}}{{\tan \theta - \sec\theta + 1}}\\ &\qquad\;= \frac{{\left( {\tan \theta + \sec \theta } \right) - \left( {\sec \theta + \tan \theta } \right)\left( {\sec \theta - \tan \theta } \right)}}{{\tan \theta - \sec \theta + 1}}\\ &\qquad\;= \frac{{\left( {\tan \theta + \sec \theta } \right)\left( {1 - \sec \theta + \tan \theta } \right)}}{{\tan \theta - \sec\theta + 1}}\\ &\qquad\;= \sec \theta + \tan \theta \end{align}\].

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