CBSE Class 10 Answered
sina +2cosa equal to 1 then prove 2sina -cosa equal to 2
Asked by hakushwah | 13 Jan, 2019, 23:23: PM
Expert Answer
Given : sinA+2cosA = 1 ....................................(1)
Required to prove : 2sinA - cosA = 2 ...........................(2)
let us use the notation, s = sinA and c = cosA
Then given trignometric equation is written as, s+2c = 1 .................(3)
let us write eqn.(3) as : s = 1 - 2c
squaring both sides of the above eqn., we have s²= (1-2c)² = 1 + 4c² -4c
4c²-4c+(1-s²) = 0 or 5c² - 4c = 0 ( because 1-sin2θ = cos²θ )
hence we have, c(5c-4) = 0 ; hence c = 0 or c=4/5 .............................(4)
if we consider c = cosA = 4/5 , then sinA = 
hence required eqn. :- if sinA = 3/5 and cosA=4/5, then 2sinA - cosA = (6/5)-(4/5) = 2/5 ≠ 2
if sinA = -3/5 and cosA=4/5, then 2sinA - cosA = (-6/5)-(4/5) = -2 ≠ 2
in eqn.(4) if we consider c = cosA = 0, then sinA = 1
hence required eqn. :- 2sinA - cosA = 2(1) - 0 = 2
Conclusion : if cosA=0 as we get in eqn.(4), then 2sinA - cosA = 2
Answered by Thiyagarajan K | 14 Jan, 2019, 08:21: AM
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