Question

State whether the following statement is true or false.

$\sec {}^{4}A(1-\sec {}^{4}A)-2\tan {}^{2}A=1$

• A. True
• B. False

Answer 1

The correct option is A True

$se{c}^{4}A(1-si{n}^{4}A)-2ta{n}^{2}A$

$=se{c}^{4}A-se{c}^{4}Asi{n}^{4}A-2ta{n}^{2}A$

$=se{c}^{4}A-si{n}^{4}A\left(1/co{s}^{4}A\right)-2ta{n}^{2}A$

$=se{c}^{4}A-ta{n}^{4}A-2ta{n}^{2}A$

$=(se{c}^{2}A{)}^2-(ta{n}^{2}A{)}^2-2ta{n}^{2}A$

$=(se{c}^{2}A+ta{n}^{2}A)(se{c}^{2}A-ta{n}^{2}A)-2ta{n}^{2}A$

$=se{c}^{2}A+ta{n}^{2}A-2ta{n}^{2}A[\because se{c}^{2}A-ta{n}^{2}A=1]$

$=se{c}^{2}A-ta{n}^{2}A$

$=1$