Question
Evaluate the following:
If $A = 45^\circ ,$ verify that:
$\sin2\text{A}=2\sin\text{A}\cos\text{A}$
If $A = 45^\circ ,$ verify that:
$\sin2\text{A}=2\sin\text{A}\cos\text{A}$
✓
Answer
$\text{A}=45^\circ$
$\Rightarrow2\text{A}=2\times45^\circ=90^\circ$
$\sin2\text{A}=\sin90^\circ=1$
$2\sin\text{A}\cos\text{A}=2\sin45^\circ\cos45^\circ$
$=2\times\frac{1}{\sqrt{2}}\times\frac{1}{\sqrt{2}}=1$
$\therefore\ \sin2\text{A}=2\sin\text{A}\cos\text{A}$
$\Rightarrow2\text{A}=2\times45^\circ=90^\circ$
$\sin2\text{A}=\sin90^\circ=1$
$2\sin\text{A}\cos\text{A}=2\sin45^\circ\cos45^\circ$
$=2\times\frac{1}{\sqrt{2}}\times\frac{1}{\sqrt{2}}=1$
$\therefore\ \sin2\text{A}=2\sin\text{A}\cos\text{A}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
state $SAS$ similarity criterion.
→In the given figure, $DE || BC$ and $\text{AD}=\frac{1}{2}\text{BD}.$ If $BC = 4.5\ cm,$ find $DE$.
→In the given figure, from a cuboidal solid metalic block, of dimensions $15\ cm \times 10\ cm \times 5\ cm$, a cylindrical hole of diameter $7\ cm$ is drilled out. Find the surface area of the remaining block. $\Big(\text{use}\ \pi=\frac{22}{7}\Big)$
→In the given figure, $CP$ and $CQ$ are tangents to a circle with centre $O$. $ARB$ is another tangent touching the circle at $R.$ If $CP = 11\ cm$ and $BC = 7\ cm,$ then find the length of $BR.$
→A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is:
Neither a heart nor a king.
→Neither a heart nor a king.
Prove the following identites:
$\big(\sec^2\theta-1\big)\big(\text{cosec}^2\theta-1\big)=1$
$ABCD$ is a trapezium in which $AB || CD.$ The diagonals $AC$ and $BD$ intersect at $O$. Prove that: $(i)$ $\triangle\text{AOB}\sim\triangle\text{COB}$ $(ii)$ If $OA = 6cm, OC = 8cm,$
→- $\frac{\text{Area}(\triangle\text{AOB)}}{\text{Area}(\triangle\text{COD})}$
- $\frac{\text{Area}(\triangle\text{AOD)}}{\text{Area}(\triangle\text{COD})}$
There are $30$ cards, of same size, in a bag on which numbers $1$ to $30$ are written. One card is taken out of the bag at random. Find the probability that the number on the selected card is not divisible by $3.$
→E and F are points on the sides PQ and PR respectively of a $\triangle$PQR. For PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm case, state whether EF || QR.
→What is the perimeter of a square which circumscribes a circle of radius a cm$?$
→