Question

Question 5
Write ‘True’ or ‘False’ and justify your answer in each of the following:
If $cosA+co{s}^{2}A=1$, then $si{n}^{2}A+si{n}^{4}A=1$

Answer 1

The statement is true.

According to the question,
$\because cosA+co{s}^{2}A=1$

$\Rightarrow cosA=1-co{s}^{2}A=si{n}^{2}A\lfloor \because si{n}^{2}A+co{s}^{2}A=1\rfloor$

$\Rightarrow co{s}^{2}A=si{n}^{4}A$

$\Rightarrow 1-si{n}^{2}A=si{n}^{4}A$

$\Rightarrow si{n}^{2}A+si{n}^{4}A=1\lfloor \because co{s}^{2}A=1-si{n}^{2}A\rfloor$