(45^ +A ) (45^ -A )= - Vidyadip

MCQ

$\sin \left(45^{\circ}+A\right) \sin \left(45^{\circ}-A\right)=$

A
$\cos A$
✓
$\frac{1}{2} \cos 2 A$
C
$\cos 2 A$
D
$\frac{1}{2} \cos A$

✓

Answer

Correct option: B.

$\frac{1}{2} \cos 2 A$

(B)
$\sin \left(45^{\circ}+ A \right) \sin \left(45^{\circ}- A \right)$
$=\frac{1}{2}\left[2 \sin \left(45^{\circ}+ A \right) \sin \left(45^{\circ}- A \right)\right]$
$=\frac{1}{2}\left[\cos \left(45^{\circ}+ A -45^{\circ}+ A \right)\right.$$\left.-\cos \left(45^{\circ}+ A +45^{\circ}- A \right)\right]$
$=\frac{1}{2}\left[\cos 2 A-\cos 90^{\circ}\right]$
$=\frac{1}{2} \cos 2 A$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from Trigonometry – II→Trigonometry – II — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

Let f : N ⟶ N defined by
$f(n)=\left\{\begin{array}{l}\frac{n+1}{2} \text { if } n \text { is odd } \\ \frac{n}{2} \text { if } n \text { is even }\end{array}\right.$ then $f$ is even

If $\frac{1}{x}+x=2 \cos \theta$, then $x^n+\frac{1}{x^n}$ is equal to

$\lim _{n \rightarrow \infty}\left[\frac{1}{n^3+1}+\frac{4}{n^3+1}+\frac{9}{n^3+1}+\ldots+\frac{n^2}{n^3+1}\right]=$

If $z _1=1-3 i$ and $z _2=2+ i$, then $\overline{ z }_1+\overline{ z }_2=$

The equation of the circle which passes through the points of intersection of the circles $x^2+y^2-6 x=0$ and $x^2+y^2-6 y=0$ and has its centre at $\left(\frac{3}{2}, \frac{3}{2}\right)$ is

The equation of a straight line passing through the points (-5, -6) and ( 3, 10) is

If $f ( x )=\frac{x^{50}}{50}+\frac{x^{49}}{49}+\frac{x^{48}}{48}+\ldots+\frac{x^2}{2}+x+1$, then $f ^{\prime}(1)=$

If $f(x)=\left\{\begin{array}{cl}x: & 0 \leq x<\frac{1}{2} \\ 1-x: & \frac{1}{2} \leq x<1\end{array}\right.$, then

Radius of circle (x - 5)(x - 1) + (y - 7)(y - 4) = 0 is

If $f(x)=\left\{\begin{array}{ll}\frac{5^x- e ^{ z }}{\sin 2 x} \quad ; \quad x \neq 0 \\ \frac{1}{2}(\log 5+1) \quad ; \quad x=0\end{array}\right.$ then