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( * ) If cos theta – 4 sin theta = 1, then sin theta + 4 cos theta =

( * )
If cos theta – 4 sin theta = 1, then sin theta + 4 cos theta = 

Grade:11

2 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
9 years ago
Hello student, Please find the answer to your question below
cos theta – 4 sin theta = 1 …....(1)
sin theta + 4 cos theta = k….…..(2)
Square and add both the equation you will get the value of k............................
Pavani Vishwanatham
26 Points
2 years ago
 Given 
Cos theta -4sin theta =1 ......( 1)
Let us assume sin theta + 4 cos theta =x ......(2) 
Add(1) and (2)
 (Cos theta -4sin theta ) + ( sin theta+4cos theta) = 1+ x 
Squaring on both sides
Cos²theta+16sin² theta - 8 cos theta .sin theta+sin²theta+16cos²theta- 8 costheta.sintheta = 1+x²
(Cos² theta + sin2theta) + 16 sin²theta + 16cos²theta= 1+x² 
1+ 16(1)= 1+ x² 
x²= 16 
x= 4

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