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If 2 cos theta + sin theta =1, then prove that 7 cos theta + 6 sin theta = 2 or 6

If 2 cos theta + sin theta =1, then prove that 7 cos theta + 6 sin theta = 2 or 6

Grade:11

1 Answers

ANSHUMAN SINGH
33 Points
5 years ago
Multiply 6 in first equation i.e 2costheta+sintheta=1 .
We get 12costheta +6sintheta=6
Now let, 7costheta+6sintheta=K
Eliminate sintheta , and get values of sintheta and costheta in terms of K
Sintheta=2K-7/5 , costheta=6-K/5
NOW we know sinsqauretheta +cossquaretheta=1 .put values here in terms of K and then a quadratic equation in K will form , on solving it we get K=6 or 2.hence prooved
 
 

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