Question

State whether the following statement is true or false.

If $\cos A+{\cos }^{2}A=1,$ then ${\sin }^{2}A+{\sin }^{4}A=1.$

• A. True
• B. False

Answer 1

The correct option is A True

Given:

$cosA+co{s}^{2}A=1$

$⟹cosA=1-co{s}^{2}A=si{n}^{2}A$..........[1]

Now,

$si{n}^{2}A+si{n}^{4}A=cosA+co{s}^{2}A=1$.....................[from $1$]