Question

If $sin\theta -cos\theta =0,\text{then the value of}si{n}^4\theta +co{s}^4\theta is:$

• A. 1/2
• B. 1/4
• C. 3/4
• D. 1/3

Answer 1

The correct option is A

1/2

We have,

$\begin{array}{c}sin\theta -cos\theta =0\\ \Rightarrow si{n}^2\theta +co{s}^2\theta -2sin\theta .cos\theta =0\\ \Rightarrow sin\theta cos\theta =\frac{1}{2}\\ Now,si{n}^4\theta +co{s}^4\theta \\ \Rightarrow {\left(si{n}^2\theta +co{s}^2\theta \right)}^2-2si{n}^2\theta .co{s}^2\theta \\ =1-2\times \frac{1}{4}\\ =\frac{1}{2}\end{array}$