Answered: Simplify the expression two ways. One…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

Simplify the expression two ways. One for each side of the equation.

tan²x* sin² x = tan²x - sin²x

Expert Solution

Step 1

Given expression is $\tan^{2} (x) \cdot \sin^{2} (x) = \tan^{2} (x) - \sin^{2} (x)$ .

Now,

$\tan^{2} (x) \cdot \sin^{2} (x) = \tan^{2} (x) - \sin^{2} (x) \frac{\sin^{2} (x)}{\cos^{2} (x)} \cdot \sin^{2} (x) = \frac{\sin^{2} (x)}{\cos^{2} (x)} - \sin^{2} (x)$ $[∵ t an (x) = \frac{\sin (x)}{\cos (x)}]$

Now multiply both side by $\cos^{2} (x)$ .

$\sin^{2} (x) \cdot \sin^{2} (x) = \sin^{2} (x) - \sin^{2} (x) \cdot \cos^{2} (x) \sin^{4} (x) = \sin^{2} (x) (1 - \cos^{2} (x)) \sin^{4} (x) = \sin^{2} (x) . \sin^{2} (x)$ $[∵ \sin^{2} (x) = 1 - \cos^{2} (x)]$

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Half-angle, Double-angle, and Product-Sum Formulae$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions