MCQ
If $\sin \theta+\cos \theta=\sqrt{2}$, then $\tan \theta+\cot \theta=$
- A1
- ✓2
- C3
- D4
✓
Answer
Correct option: B.
2
(B)2
$
\begin{array}{l}
\text { We have, } \sin \theta+\cos \theta=\sqrt{2} \\
\Rightarrow \quad(\sin \theta+\cos \theta)^2=2 \\
\Rightarrow \quad \sin ^2 \theta+\cos ^2 \theta+2 \sin \theta \cos \theta=2 \Rightarrow 1+2 \sin \theta \cos \theta=2 \Rightarrow 2 \sin \theta \cos \theta=1 \Rightarrow \sin \theta \cos \theta=\frac{1}{2} \\
\therefore \quad \tan \theta+\cot \theta=\frac{\sin \theta}{\cos \theta}+\frac{\cos \theta}{\sin \theta}=\frac{\sin ^2 \theta+\cos ^2 \theta}{\sin \theta \cos \theta}=\frac{1}{\sin \theta \cos \theta}=2
\end{array}
$
$
\begin{array}{l}
\text { We have, } \sin \theta+\cos \theta=\sqrt{2} \\
\Rightarrow \quad(\sin \theta+\cos \theta)^2=2 \\
\Rightarrow \quad \sin ^2 \theta+\cos ^2 \theta+2 \sin \theta \cos \theta=2 \Rightarrow 1+2 \sin \theta \cos \theta=2 \Rightarrow 2 \sin \theta \cos \theta=1 \Rightarrow \sin \theta \cos \theta=\frac{1}{2} \\
\therefore \quad \tan \theta+\cot \theta=\frac{\sin \theta}{\cos \theta}+\frac{\cos \theta}{\sin \theta}=\frac{\sin ^2 \theta+\cos ^2 \theta}{\sin \theta \cos \theta}=\frac{1}{\sin \theta \cos \theta}=2
\end{array}
$
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 one root of the equation $4\text{x}^2-2\text{x}+(\lambda-4)=0$ be the reciprocal of the other, then $\lambda=$
→For the data $2,9, x+6,2 x+3,5,10,5$; if the mean is 7 , then the value of $x$ is :
→If the altitude of the sun is $60^\circ,$ the height of a tower which casts a shadow of length $90m$ is :
→In the given figure, PQR is a tangent to the circle at Q, whose centre is O and AB is a chord parallel to PR, such that$ \angle\text{BQR} = 70^\circ.$ Then, $\angle\text{AQB}=?$
→Choose the correct answer from the given four options: A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6000 tickets are sold, how many tickets has she bought?
The points $A(4, -1), B(6, 0), C(7, 2) $ and $D(5, 1)$ are the vertices of a
→The degree of polynomial having zeroes $-3$ and $4$ only is :
→In the given figure, $\text{ABCD}$ is a trapezium whose diagonals $AC$ and $BD$ intersect at $O$ such that $OA = (3x - 1)cm, OB = (2x + 1)cm, OC = (5x - 3)cm$ and $OD (6x - 5)cm.$ Then $x =?$
→A bag contains 3 white, 4 red and 5 black balls. One ball is drawn at random. What is the probability that the ball drawn is neither black nor white?
$\sqrt{\frac{1-\sin\text{A}}{1+\sin\text{A}}}=?$
→