MCQ
If $\sin\text{3A}=\cos(\text{A}-10^\circ)$ and $\text{3A}$ is acute then $\angle\text{A}=?$
- A$35^\circ$
- ✓$25^\circ$
- C$20^\circ$
- D$45^\circ$
✓
Answer
Correct option: B.
$25^\circ$
$\sin\text{3A}=\cos(\text{A}-10^\circ)$
$\Rightarrow\cos(90^\circ-\text{3A})=\cos(\text{A}-10^\circ)$
$\Rightarrow90^\circ-\text{3A}=\text{A}-10^\circ$
$\Rightarrow\text{4A}=100^\circ$
$\Rightarrow\text{A}=25^\circ$
$\Rightarrow\cos(90^\circ-\text{3A})=\cos(\text{A}-10^\circ)$
$\Rightarrow90^\circ-\text{3A}=\text{A}-10^\circ$
$\Rightarrow\text{4A}=100^\circ$
$\Rightarrow\text{A}=25^\circ$
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
If $PA$ and $PB$ are two tangents to a circle with centre $O,$ such that $\angle\text{AOB} = 110^\circ,$ find $ \angle\text{APB}$ is equal to
→Choose the correct answer from the given four options: Consider the following distribution:
the frequency of the class 30-40 is:
|
Marks obtained
|
Number of students
|
|
More than or equal to 0
|
63
|
|
More than or equal to 10
|
58
|
|
More than or equal to 20
|
55
|
|
More than or equal to 30
|
51
|
|
More than or equal to 40
|
48
|
|
More than or equal to 50
|
42
|
If $\cos\text{A}+\cos^2\text{A}=1$ then $\sin^2\text{A}+\sin^4\text{A}=?$
→A polynomial whose sum and product of zeroes are $-4$ and $3$ is :
→In $\triangle A B C, D E \| B C$ (See Fig. 7.30). If $A D=4 cm, A B=9 cm$ and $A C=13.5 cm$, then the length of $E C$ is
→The zeroes of a polynomial $x^2+ 5x - 24$ are :
→If $x=a \sec \theta$ and $y=b \tan \theta$, then $b^2 x^2-a^2 y^2=$
→If $p$ and $q$ are co-prime numbers, then $p^2$ and $q^2$ are
→The arithmetic mean of 1, 2, 3, ..., n is:
If $\sin \theta=\cos \theta\left(0^{\circ}<\theta<90^{\circ}\right)$, then the value of $\sec \theta \sin \theta$ is
→