MCQ
$3 \sin ^2 20^{\circ}-2 \tan ^2 45^{\circ}+3 \sin ^2 70^{\circ}$ is equal to:
- A$0$
- ✓$1$
- C$2$
- D$-1$
✓
Answer
Correct option: B.
$1$
$3 \sin ^2 20^{\circ}-2 \tan ^2 45^{\circ}+3 \sin ^2 70^{\circ}($ Given $)$
$\Rightarrow 3\left(\sin ^2 20^{\circ}+\sin ^2 70^{\circ}\right)-2 \tan ^2 45^{\circ}$
We know that, $\sin 70^{\circ}=\sin (90-20)^{\circ}=\cos 20^{\circ}$ and $\tan 45^{\circ}=1$
Substituting these values in equation $(1),$
we get, $\Rightarrow 3\left(\sin ^2 20^{\circ}+\cos ^2 20^{\circ}\right)-2$
Also, by an identity $\sin ^2 20^{\circ}+\cos ^2 20^{\circ}=1$
$\Rightarrow 3-2=1$
Hence, the correct option is $(b).$
$\Rightarrow 3\left(\sin ^2 20^{\circ}+\sin ^2 70^{\circ}\right)-2 \tan ^2 45^{\circ}$
We know that, $\sin 70^{\circ}=\sin (90-20)^{\circ}=\cos 20^{\circ}$ and $\tan 45^{\circ}=1$
Substituting these values in equation $(1),$
we get, $\Rightarrow 3\left(\sin ^2 20^{\circ}+\cos ^2 20^{\circ}\right)-2$
Also, by an identity $\sin ^2 20^{\circ}+\cos ^2 20^{\circ}=1$
$\Rightarrow 3-2=1$
Hence, the correct option is $(b).$
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
The perimeters of two similar triangles $A B C$ and $P Q R$ are 56 cm and 48 cm respectively. $\frac{P Q}{A B}$ is equal to
→The pair of linear equations y = 0 and y = - 6 has:
The sum of first 40 positive integers divisible by 6 is:
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
→$2.13113111311113 ... $ is :
→A steel wire when bent in the form of a square enclosed an area of $121 cm ^2$. If the same wire is bent in the form of a circle, then the circumference of the circle is
→After an examination, a teacher wants to know the marks obtained by maximum number of the students in her class. She requires to calculate _____ of marks.
If $9$ times the $9^{th}$ term of an $A.P$. is equal to $11$ times the $11^{th}$ term, then its $20^{th}$ term is :
→If $a \cos \theta+b \sin \theta=4$ and $a \sin \theta-b \cos \theta=3$, then $a^2+b^2=$
→If $29x + 37y = 103$ and $37x + 29y = 95$ then :
→