If $\sin \theta+\cos \theta=m$ and $\sec \theta+\operatorname{cosec} \theta=n$, then $n(m+1)(m-1)$ is equal to
44 views
0 Votes
0 Votes

If $\sin \theta+\cos \theta=m$ and $\sec \theta+\operatorname{cosec} \theta=n$, then $n(m+1)(m-1)$ is equal to

(A) $m$

(B) $n$

(C) $2 m$

(D) $2 n$

1 Answer

0 Votes
0 Votes
 
Best answer

SOLUTION —

Given,$\sin \theta+\cos \theta=m$

$\begin{array}{l}\sec \theta+\operatorname{cosec} \theta=n \\n(m+1)(m-1)=n\left(m^2-1\right) \\=(\sec \theta+\operatorname{cosec} \theta) 2 \sin \theta \cos \theta \\\left(\because m^2=1+2 \sin \theta \cos \theta\right) \\=\frac{\sin \theta+\cos \theta}{\sin \theta \cos \theta} \cdot 2 \sin \theta \cos \theta=2 m \\\end{array}$

So, The correct option will be (C).

RELATED DOUBTS

1 Answer
0 Votes
0 Votes
30 Views
1 Answer
0 Votes
0 Votes
51 Views
1 Answer
0 Votes
0 Votes
56 Views
Peddia is an Online Question and Answer Website, That Helps You To Prepare India's All States Boards & Competitive Exams Like IIT-JEE, NEET, AIIMS, AIPMT, SSC, BANKING, BSEB, UP Board, RBSE, HPBOSE, MPBSE, CBSE & Other General Exams.
If You Have Any Query/Suggestion Regarding This Website or Post, Please Contact Us On : [email protected]

CATEGORIES