Question

The value of sin2θ+cos2θ at θ=30∘ & 60∘ is respectively.

• A. $\frac{1}{4}\&\frac{3}{4}$
• B. $\frac{3}{4}\&\frac{1}{4}$
• C. $1\&1$
• D. $0\&\frac{3}{4}$

Answer 1

The correct option is C $1\&1$

When $\theta ={30}^{\circ }$, $sin\theta =\frac{1}{2}$ and $cos\theta =\frac{\sqrt{3}}{2}$
$\therefore si{n}^2\theta +co{s}^2\theta ={\left(\frac{1}{2}\right)}^2+{\left(\frac{\sqrt{3}}{2}\right)}^2=\frac{1}{4}+\frac{3}{4}=\frac{4}{4}=1$
When $\theta ={60}^{\circ }$, $sin\theta =\frac{\sqrt{3}}{2}$ and $cos\theta =\frac{1}{2}$.
$\therefore si{n}^2\theta +co{s}^2\theta ={\left(\frac{\sqrt{3}}{2}\right)}^2+{\left(\frac{1}{2}\right)}^2=\frac{3}{4}+\frac{1}{4}=\frac{4}{4}=1$