Question

The value of 2sinθ can be 1 a a , where a is a positive number, and a ≠ 1

Answer 1

Let 2sin theta - cos theta = x ……(A)

Given : sin theta + 2cos theta = 1 …..(B)

Now,addition of squares of (A) and (B) gives

(2sin theta -cos theta)^2 + (sin theta + 2cos theta)^2 = x^2 + 1

=> 4sin^2 theta -4sin theta× cos theta+cos^2 theta +sin^2 theta +4sin theta × cos theta +4cos^2 theta = x^2 + 1

=>5sin^2 theta + 5 cos^2 theta =x^2 +1

=> 5(sin^2 theta +cos^2 theta)=x^2 + 1

=> x^2 + 1 =5 { Since sin^2 theta + cos^2 theta= 1