Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

If  2 \cos x + \sin x = 1, then value of 7 \cos x + 6 \sin x  is equal to

Option: 1

2 or 6


Option: 2

1 or 3


Option: 3

2 or 3


Option: 4

None


Answers (1)

best_answer

 \\2 \cos x + \sin x = 1 .......(i) \\ 4 \cos ^2 x = (1-sin x )^2 \\4 - 4 \sin ^2 x = 1 + \sin ^2 x - 2 \sin x \\ 5 \sin ^2 x - 2 \sin x -3 = 0\\ ( \sin x - 1 ) (5 \sin x + 3 ) = 0 \\ \Rightarrow \sin x = 1 , \sin x = -3/5 \\ \because \cos x = \frac{1- \sin x }{2} (from (1)) \\\\ \because when \: \:

\\\sin x = 1 \\ 7 \cos x + 6 \sin x = 7 \frac{1- \sin x }{2} + 6 \sin x \\\\ = 7 \left ( \frac{1-1}{2} \right ) + 6 \times 1 = 6

\\and \: \: when \: \: \sin x = -3/5 \\ then \: \: 7 \cos x + 6 \sin x = 7 \left ( \frac{1+ 3/5 }{2} \right ) - \frac{6\times 3}{5} = \frac{28-18}{5} = 2

Posted by

jitender.kumar

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Mains 2026: BTech Electrical Engineering cut-offs highest at NIT Rourkela among all NITs, IIITs, GFTIs
anam-khan

JEE Main 2026 session 1 results, final answer key today; what is NTA score?
anam-khan

JEE Main 2026 Result Date LIVE: NTA delays Session 1 results; ‘What kind of clownery is this?’ ask candidates

Latest Question