Math, asked by swathi2210, 1 year ago

if a cos theta- b sin theta =c show that +- root of a square + b square - c square

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Answers

Answered by suresh3360
1
I am considering theta as 't' for the purpose of clarity...

First square both the sides of provided equation.
==> {acost - bsint}^2 = c^2
==> a^2(cost)^2 + b^2(sint)^2 -2abcostsint=c^2---eq(1)
Now consider LHS of the equation which should be proved right.Let that be equal to 't'

y= {asint+bcost}
y^2=a^2(sint)^2 + b^2(cost)^2 + 2absintcost---eq(2)

By adding equations eq(1) and eq(2) we get

a^2{(sint)^2 + (cost)^2} + b^2{ (sint)^2 + (cost)^2}=y^2 + c^2

==> a^2 + b^2 = y^2 + c^2
===>y=+/-
 \sqrt{ {a}^{2}  +  {b}^{2}  -  {c}^{2} }
Hence proved
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